Good puns are a valuable commodity and even fairly serious game use them, so it's not like anybody is ever turning down great puns for no reason. So the good stuff, if they exist, is no different than what any other game would already attempt to do.

A game is the sum of its parts. If the music of FF14 was worse than what it is now, you'd probably still play the game, but it wouldn't be as enjoyable. Likewise, although quest names are a very minor part of the game, they're what you see first so they do make an impression. If a quest name made you think 'wow that's dumb', that's still worse than a generic quest name like "Titan (Hard mode)", which you'll almost certainly be indifferent to.

It seems to me whoever did the localization figured since he can't actually make great puns, he'd go for quantity and hope he'll accidentally stumble something that's the equivalent of "FOR GREAT JUSTICE", but I'd argue he missed on all his attempts.