This will result in people excluding certain classes and will make the Duty Finder a big risk factor when it comes to clearing content. A example would be: BLM joins Duty Finder and gets Ifrit this will make the BLM useless to the group and force the other 7 players to play with someone who will do almost no damage.
Another thing is, this will force players to level other classes/jobs so they can experience certain contents. I love leveling all my classes, but some players prefer only leveling one or two classes. It would not be fair towards them to force them to spend alot of time leveling other classes. Freedom of choice is one of the things that every mmorpg has, making certain classes useless for dungeons/trail will only scare away players from this game.
Weakness to elementals or absorption of elemental spells would work in single player games, because your not playing with others, but in a mmorpg, I find this a bad idea.