There's a game outside Abyssea where MP is finite and some of the new Voidwatch NMs have clearly been to the gym. Obviously not everything needs PLD's unique level of survivability, but not everything should, because then you've created the opposite problem. Not everything should be dependant on one job (tanking, healing, whatever), just like like one job shouldn't be useless at everything.

I agree that most of Paladin's ability timers (Divine Emblem's timer can only really be described as a joke) need to be retooled in the face of abilities like Counterstance and Third Eye. However, I feel that, in the interim, making Cover a job trait would be a good stop gap. It's the only ability that has always been essentially worthless, and it's the one thing I think can be adjusted without everyone screaming OMG BROKEN. While I don't think Paladin's offense is the worst in the game, I do think that any buff to it would be stepping on the toes of jobs like SAM, MNK and WAR, and pulls Paladin out of the role SE has been trying to carve out for it.

Making Cover a job trait won't necessarily make Paladin more desirable, but it would undeniably make it more useful, and it certainly wouldn't make it any less desirable.