Well Monster Hunter has its own set of rules in its own universe. I agree it doesn't make sense but it makes for some really fun gameplay. You actually do have to surface for air occasionally but you can swim for unnaturally long periods of time underwater.

Final Fantasy X though I never questioned. Sure it was never explained but they presented it in such a way that I never needed an explanation. People can swim really fast and breathe underwater in Spira, why not? I guess sometimes the more attention a game brings to something and the more it tries to explain the more plausible the explanation needs to be. If it's just an accepted law of that particular world and everyone treats it as such then little attention is even brought to it. It's a fantasy world, they do it because they can lol.

Final Fantasy XIV is a world filled with magic that has little explanation. Spell casting is often given little explanation in the game as it's just an accepted thing you can do. Being able to "die" and be resurrected at a big floating crystal is the same. While you're at it why don't you add surviving being stomped on by a giant buffalo to the list? All things that we simply accept because that's just how they are in the world. Being able to breath underwater be it through spell, gear or just because is just another one of those things.