Who thought this was a good idea and why?

Its to surprise and counter his attackers that naturally pick a certain typing to beat the specific pokemon, and then are hit with a completely unexpected move type that hits them super effectively.

In this case...they use water to counter your fire type, then get hit with a massive grass move that does allot of dmg to then, its more effective than getting hit with a fire move that they expected.

Arcanine is another one, he can learn wild charge and surprise water types with a big electric move.

I personally find the idea quite interesting myself...they have clearly done this sort of thing for a reason...to be effective into the common attackers vs the pokemons type, either way they have not just picked these moves at complete random.

As for wanting them? No...not really, if i evolve a high IV i would prefer stab moves, mostly with offence in mind. But maybe if its going to be a defender these wierd moves can be usefull. Also TMs exist now so nothing is truly lost if you get a move you dont want.

Solar Beam, being a grass move, is super-effective versus Water, Rock, and Ground, all those types which are counters to Typhosion.

It's a nice idea in theory, I suppose, but probably doesn't work well in practice since he has more value as an attacker instead of a defender.

It's a concept from the main games that does not translate well to the gameplay in Go.

In the main games, where each mon can have four moves, it's often a good idea to hold a surprise in your back pocket to take your opponent off guard. But in Go, the only 'strategy' is tapping your screen and knowing when to swipe to dodge. And we're limited to only two moves. So here, they serve only as yet another mechanism by which the RNG gods can smite the chronically unlucky among us.

For sure Lapras doesn't like it!

It's as annoying for an attacker to meet that kind of mon in a gym as it is meeting a Shadow Ball or Dark Pulse Weezing in a raid.

A waste of defensive moveset. Unlike most defensive movesets being double/tripple bar, a single bar charge move is unlikely to go off if the attacker uses a high CP counter. Useless

Solar Beam is a really good move against many of Typhlosion's counters. In the main series game, Solar Beam could only be taught by a TM and a Sunny Day/Solar Beam Typhlosion can be useful competitively. Sunny Day made the battle "sunny" which allowed Typhlosion to use SB without charging it up for a turn (normally, SB is charged for a turn and then fired on the second turn). This had excellent sweeping potential because SB was such a powerful grass-type move that that charging-turn balanced its damage output. In PokemonGO, it's much less useful of a move because the battle system is a lot more shallow (tapping/swiping) and not turn-based.

IMO, Niantic brought over a lot of things from the main series games that have really no use in PokemonGO because how different it is from the main series. I would say that these counter-type charge moves (and other things) in PokemonGO are just remnants of the games origin and not because someone thought it was "a good idea".

Why would a he need 3 different fire moves? and why?

Good idea? Powerful grass move that it can learn translated over from the main series and covers its water, ground, and rock weakness...do you suggest it learn Wild Charge or Thunder Punch (moves it can actually learn from the main series) because I don't know what else you would put on it? Sure, it's not going to fire it off as a defender. But we are no longer in the defending era. Why? Solar beam again is power move, if you roll it, invest in a different typhlosion. Or you could TM it I supposed but imo it's not worth it unless you really love it. Save your SB one for PVP.

Grass covers all of fire's weaknesses.
But SoB is too easy to dodge, and it might not fire at all!