Note that all your team have 2 bar move and similar dps. This is why dodging would hurt you in most cases, but most teams aren't like that. Dying with a full energy bar hurt your dps and can usually be avoided with a dodge at the right time.
For example, if your team had 3 gengars up front and 3 ttars on the back, your time would have been better if you dodged with the gengars because their dps is better than the ttars, so every extra second Gengar is on the field gain you time.
Another way to put it is that if there is a big dps difference among your team, you want to maximize the TDO of your high DPS counters, and the way to do it is Dodge. If you ever do a unique 6 or pokedraft challenge you will soon realize that dodging significantly improve your time if you dodge with the right Pokemon at the right time.
No-dodge Alakazam solo, 18 seconds left
I'm going to post a few of these from time to time, as they occur, in order to debunk the myth that dodging is necessary or even useful for most L3 solo raids.
My team was as follows:
L37 Mewtwo 3773 PC/SB
L40 Gengar 2541 SC/SB
L37 Mewtwo 3724 C/SB
L34 Gengar 2387 H/SB
L33.5 Gengar 2343 H/SB
L38 Alakazam 2775 PC/SB*
*never used
The boss was a PC/FB Alakazam. I dodged ZERO times. Note that the Alakazam in the #6 slot was never needed, and the Gengar in the #5 slot (see photo) was barely nicked, and didn't even need to launch his first SB.
Somebody posted yesterday that you need to dodge every charge move against Alakazam. I'm flabbergasted by that statement. Had I dodged, every dodge would have added a few seconds to my time-to-win, and if I dodged five or six times, I would have timed out. Without dodging, I barely used the fifth mon, and I won with 18 seconds left (probably more like 20 when the knockout punch actually landed).
Obviously, different boss movesets have different characteristics, and I do think that C/FB 'Zam requires MINIMAL dodging of focus blast (like maybe two or three dodges at most), but dodging is unnecessary against every other Alakazam moveset if you have a decent team that hits hard. The same goes for almost every other L3 boss. I regularly beat Machamp with 50+ seconds left, and I never dodge.
If you are losing L3 raids that you should be able to solo, and you are dodging, that is probably why.

Answers
Disagree. What you want to maximize, regardless of your team, is the team's total DPS. In your example, if you squander the DPS of the Gengars by dodging in order to keep them in the fight longer, their DPS will quickly fall below that of, say, no-dodge T-tars (but there is no reason to use Ttars against PC/FB 'Zam).
Don't take my word for it; look at simulations with no-dodge and various dodge scenarios, and you'll see that no-dodge is almost always faster. People generally way underestimate how much dodging penalizes DPS.
The point of this is for the benefit of people who have bought into the BS that dodging is necessary to win solo raids, like the guy yesterday who was advising that people need to dodge every charge move against Alakazam. If you are going to cherrypick counter examples with suboptimal teams (why would anyone use Ttar against PC/FB 'Zam?), or talk about challenges that aren't about winning raids as efficiently as possible, then I'm sure you will find some cases where dodging is beneficial.
For the average player who is wondering why they are failing at L3 solos with their best team, and they are trying to dodge a lot (and probably missing dodges occasionally), dodging almost always hurts them more than it helps them.
To your examples showing the DPS of the Gengars, the no-dodge DPS looks higher to me (although the sample size isn't really big enough to tell), and that assumes no human error with regard to the dodging.
As an example for most of what I said, watch this donphan solo, as part of the pokedraft:
https://m.youtube.com/watch?v=0h4uYKXghQ8&t=5s
It's sunny weather and Venusaur is by far the highest dps counter in the team. My strategy coming into the raid was to dodge as much as possible with Venusaur to maximize his TDO, and not dodge with anyone else (though in retrospect dodging with victreebel would probably help, since it would reduce the time swampert is on the field). Also note the dodge with Moltres, this is a common occurrence with 1 bar moves, and dying with a full bar plummet the dps. Not dodging with him would cost me somewhere between 5-10 seconds.
You don't need maxed Lugias against Machamp. You need decent (say L35) Alakazams and Espeons with C/FS, and maybe one L30 Lugia as an anchor in the last slot. If it has close combat, you don't even need the Lugia. Survivability is a lot less of an issue if you beat the boss with nearly a minute left.
You won't even nearly beat Machamp with almost a minute left with 5 L35 Alakazams/Espeons and a L30 Lugia anchor if you don't dodge, the Lugia lowers your DPS way too much for that. If you're running an anchor with lower DPS, you would beat the boss faster by maximizing the damage your better counters deal and this would involve dodging DP/HS to make sure they each fire 2 FS and then die shortly afterwards.
That is because every Pokémon in your party resists Focus Blast, and Psycho Cut is a joke compared with Confusion, which hits like a truck. I highly doubt your team can beat Shadow Ball Alakazam without dodging.
If you have the Lugias, then yes, you don't need to dodge against even Dynamic Punch Machamps.
I have beaten both SB movesets multiple times without dodging. Not with this team, obviously. I have four B/C T-tars at my disposal for the SB movesets.
Of course you need a team that is up to the task. The point you are missing is that most cases, a team that is good enough to win with dodging will win faster without dodging, unless it simply can't survive the battle without dodging. Even then, DPS for the no-dodge team will almost always be higher.
For dodging, I think it comes down to something as simple as this: skilled dodging saves HP. Thus, skilled dodging requires less HP to begin with, which means, if you dodge, you can get away with lower level attackers.
I found with Machamp that as I powered up my attackers more and more, dodging became completely unnecessary. Even in cases where I was going up against a boosted Dynamic Punch Machamp, I would faint out, rejoin with a B team (while the boss regenerated health), and still do enough damage to win. This is impossible with level 30 attackers, but fairly straightforward with enough level 35-40 attackers.
So, dodge if your attackers are lower level. Otherwise, dodge if you enjoy the challenge and satisfaction of a successful dodge.
If you enjoy the challenge and satisfaction of a successful dodge, battle gyms. When there is no hard time limit, dodging is absolutely beneficial. No question.
Maybe you've hit on the real reason people dodge in solo raids, despite all the evidence that it is usually an inferior strategy. They enjoy dodging, and want to convince themselves that they are using "skill," despite the hard mathematical evidence that they are using an inferior strategy.
I find it fascinating that people feel compelled to run simulations until they can come up with a rare example where dodging actually improves DPS, assuming absolutely no human error. I'd like to see some screenshots or videos where people actually show how much time they had to spare against the boss with their dodging strategy.
The simple fact you're missing here is that the DPS a mon deals is largely related to how much energy is wasted when it dies since charge moves deal so much better DPS than any fast move. If you don't dodge, you will often end up with Alakazams or Espeons that die with 50+ energy in their bar and that's horrible. I can prove it to you by math:
Against a BP Machamp, L40 Alakazam with C/FS deals 381 damage in 12,3s with 6 Confusion and 1 Future Sight, reaching a DPS of 30,97 for the cycle. If it dies after 3 more Confusions, it dealt 477 damage in 17,1s, its overall DPS lowering to 27,9, a 10% difference. For reference, that's a fair bit larger than the average DPS difference between Mewtwo and Alakazam.
The only way you can influence this factor on DPS is by dodging smartly, the rest is RNG on when the boss decides to use its charge moves to kill your attackers. But if you aren't maximizing your energy usage by dodging when it's good to do so, you're doing suboptimal DPS.
"Maybe you've hit on the real reason people dodge in solo raids, despite all the evidence that it is usually an inferior strategy. They enjoy dodging, and want to convince themselves that they are using "skill," despite the hard mathematical evidence that they are using an inferior strategy."
I actually partially agree here, but there are indeed scenarios where dodging allows you to get 1 more charge move off. Especially with single-bar charge move glass cannons.
I didn't in gym battles occasionally, but there is so little reward in gym battles that I lose interest. I think my point is this: if every battle is just a tap fest, I would get bored. I do extra things to keep myself entertained like dodging, unique teams, no weather boost, no super effective, 1 v. 1, etc. You could just blast a Scyther with level 40 Tyranitars, but I find it more fun to use other stuff like Raikou and Sudowoodo just because I can.
Marginal teams can be a lot of fun. I did a Scyther on Friday with Piloswine, Walrein, Arcanine, Rapidash, Ninetales and Manectric, no weatherboost. Ended up being pretty close because I lost a full 10 seconds at the start to network error. Slotting in 6 SD tyranitars and only needing the first 2 anyway would be beyond boring.
Psycho Cut Focus Blast requires 0 dodging even with 3 Gengar and 3 Mewtwo. It's completely natural that this happens. Confusion Focus Blast however needs perfect dodging if the bulk of your team isn't consisted of Mewtwos or is heavily consisted of Gengars and Banettes (Gengar is auto killed in 4 or 5 confusions).
As for Future Sight and Shadow Ball, if you have enough Tyranitars and Mewtwos against FS and enough Tyranitars against Shadow Ball you don't even need to dodge.
Before weather-boosting and the dedicated charge button, Level 30 me had to know when to dodge and when to tank. I could not have defeated Machamp and Gengar (and eventually Alakazam) without strategic dodging.
Now that I'm closing in on level 39 with mostly level 35+ Pokemon I can more comfortably tank those raid bosses. Your blanket no-dodging suggestion tells me that you and your Pokemon are high enough level to do so but remember, not everyone is yet.
To solo C/FB Alakazam without dodging, you need a team of 5 L40 PC/SB Mewtwos or 6 L35 PC/SB Mewtwos and that takes significant resources which most players don't have or won't want to invest solely into that M2 team. It's a pretty unique case since its split moveset ensures that every other top counter to it gets completely demolished.
I screwed up today vs a Hitmonlee, boosted Close Combat. Mewtwo level 40 15a/14/15 PC/ShB (didn’t have time to change PC to Confusion). Mewtwo lvl 40 15a/11/15 PC/ShB. Perfect level 40 Gardevoir C/DG. THEN, maxed Gengar SC/ShB 14a/12/11, another maxed SC/ShB 14a/4/15. No dodges. Clock started 4 sec slow and clock ended 3 sec early...needed 1 more second. The countdown clock had about 120sec when I decided to do it. I needed to check that SC/ShB Gengar not very good against Hitmonlee, plus change the Mewtwos to Confusion. Playing for free, so I do legendaries with my daily pass, not any plan/researching to do the tough tier 3s
Couple things to point out. It all depends on the situation. No one is right or wrong about dodging. Dodging helps trainers at lower levels who are not blessed with Shadow Claw Gengar, or Mewtwo vs Alakazam. Usually these players are level 30 at most, and have a team of Espeon, maybe one Alakazam, no legendary, and maybe a Hex Gengar. Or maybe all they have are a few Dark Tyranitar and they have to use those. Try your simulation with that team and let us know how it goes.
Level 35+ players usually have no issues with any level 3 raids. With the right counters dodging is not needed. A full team of Maxed out Kyogre with Hydropump could take out a Claydol. However not everyone has that team.
To beat some raids you actually have to NOT dodge to build up your charge move. However no one can say whether dodging or not is ideal. One player can post a raid with dodging on a certain boss, someone can do another raid with no dodging. It’s not about math, or whether who is right or wrong. It’s about what you have available and the situation.