Hmm, this would tip this game quite a bit more into being like every other MMO. Stat boosts should realistically be reserved for gear and buffs from another class like BRD for example, this would make it far too easy to make the game less group oriented. This as a gil sink would be ok if it didn't essentially unbalance things in the long run.

Gil sinks would be things like Dynamis from XI (used to cost 1 million per glass, multiple groups could end up buying a glass = hundreds of millions gone just like that) or Limbus -- Basically content that cost you a decent amount of gil to participate in.

It's not exactly like Fatigue, it's more like how MMOs award bonus XP for not playing their game -- Eventually you'll normalize back to your usual levels if not lower in some cases, however being reduced to no damage is like the fatigue system that people ironically complained about (given the push for catering this game to people who can only play 5 hours a week) so yeah, I'd vote no as well.