The end result would either be BLM OP or BLM useless, and both of them are bad for the game. There always has to be a balance and you can't limit 1 class from playing half the content because half of the fights have element resistance and you'd rather take Melee instead. You also don't want a repeat of 1.0 that would result in people only wanting BLM because of element weakness abuse. Every class has to be able to play every bit of content.

As for BLM casting elements on Melee/Bard/Tanks, I'd love that. Cast a 15 second element onto a players weapon and have them deal an extra 20% elemental damage with an amazing elemental/audio effect on their weapon while you receive a 20% spell speed reduction. Give them a resistance to the buff of 60 seconds and give the spell a 15 second cool-down, that way they have to cycle through DPS or even Tanks to help increase damage for enmity.

However, only reason I love it is because I'm a sucker for nostalgia and Vivi is my favorite FF character so... yeah. If they can implement something and keep balance, that's great, but it's much harder to keep balance than the average player thinks. Making everyone the same isn't the same as balance and making everyone unique can cause a lot of balance issues. Making everyone the same with gimmicks is also a tried-and-failed method, too. Single player is a much easier place to implement this as balance isn't really much of an issue, but in multi-player it's huge.