I haven't been following the community tightly as I used to be recently, but it seems to me that healers are already losing their minds over something both RDM & SMN (Non-healer jobs) are still easily pulling off. Heck, without the MP limit, RDM could spam rezzes to multiple players in a few seconds (Dualcast: Cure/Attack + Rez)
Do you honestly think Phoenix Downs are going to keep the party's HP up during dungeon pulls? Even if we consider the 'Slippery slope' in which the devs allowed it to be used in 8-man content. It will be difficult for a player (Tank or DPS) going around rezzing several players and maintaining their HP as a non-healer, and that's not counting the enrage or the mechanics involved.
As a fan of RPG elements, and of several Final Fantasy games, I'm glad to see Phoenix Downs earning a spotlight and an emphasis on coming prepared with items in your inventory rather than it being pure skills & spells.
Besides, what are we going to do when a healer messes up and dies mid-fight in a dungeon? Wipe and restart the boss again just because of one player who wants to feel his role is fulfilled? I'd rather have an emphasis on individual accountability and contribution.
Your job role is 'Healer' not 'Ressurector' so instead of worrying about a non-healer rezzing. It might be better to keep everyone alive so they don't have any need to rez in the first place. Granted, some mechanics can one-shot players, but still healers are needed as healers, not as rezzing machines (Otherwise, there'd have been no need to bring healers instead of SMN & RDMs)
I do agree with healers that there might be better ways to grant healers the complexity they need (I still find EW AST Rework to be ridiculous), but it's not about resurrections at all. Other games (WoW and GW2, for example) had resurrections in the hands of other roles and players but still had functional healer roles and need to bring one or more.