Power up cost pro and cons

1. It costs a lot more stardust and candies to power pokemon past 30, as you know, and since the raids are a big focal point of this game, a popular mindset is to obtain 6 pokemon for each raid boss counter @ lv30 and then power them up. Since power ups past 30 provide a power up result that is half the power up of lv 30 or below, this means that a lv39 pokemon would be the same as a lv34.5 if power ups past lv 30 gave the same amount of stat boosts as pre-lv 30 power-ups. In other words, the difference between a lv 20 and a lv 29 is two times greater than the difference between a lv30 and 39. I probably could have worded this point differently, but I hope it gets the message across
2. Break point-watch this video below; this guy does an excellent job of explaining what they are and provides links in the description that will allow you to calculate the level your pokemon needs to be in order to get that break point against a specific raid boss or a defender. Break points are essentially levels that your pokemon needs to be, in certain match-ups, to deal out a more damage. For example, if you have a charizard, your charizard would need to be level X to get that extra break point against blissey but level Y to get that extra break point against exeggutor but level Z to get that extra break point against gengar.

https://www.youtube.com/watch?v=0qQpGUieWO8

Break points are determined by the attacker's attack stat and the defender's defense stat

Many fast-move breakpoints aren't reached until well after L30, so the L30 mindset needs to really die already. Now, in particular matchups a L30 may be powered up enough to deal max damage with their fast move and if that's the case then it's okay, but that's not always the case.

Like the above poster mentioned these breakpoints shift depending on the target, so in some cases a trainer who only powers stuff up to L30 isn't even getting full damage from their fast-move--not where you wanna be.

To answer the other part of your question a L39/40 does ~6-9% more damage (this comes from Charged Moves) than a L30--this percent increase will be even higher if compared to a L30 that is not doing max damage with its fast move. To me this is a considerable amount and is worth it imo, but you must keep in mind this school of thought will cost you great amounts of stardust. I'm good with that as I've almost completed everything I wanna train from Gens 1 & 2

As someone who has maintained maxed mons for months allow me to say it does make a difference. Do I have the exact stats and figures. No. Maybe its true that damage gets capped at a certain point. What those people fail to tell you is the bulk you gain keeps you alive longer -- greatly so with effective dodging. Anyone who says its not worth powering up a mon past 30 is a noob, plain and simple. Should PvP ever come out I will back that statement up. Until then perhaps there's some truth to it. In raids quantity often overrules quality. That said do you think those legit players who duo Tyranitar and Moltres are using level 30 Machamps and Golems?