No - that just subjects the monk to a mean RNG which is never good. As I said, better to think of it as Jedi Mind Tricks (or Psychic Neuralizer) than Human Opposum. You can keep using the JMT/Neuralizer and they'll keep forgetting you're there.
Though I'm fine with a class of mobs (undead spring to mind) being immune to FD (or ES if we're going the Jedi Monk route). But if you make undead immune to monk FD then you have to fiddle with Necro/SK FD so it doesn't become better than Monk FD (Necro/SK would get a different skill Feign Undeath that maybe didn't work against animals or whatever).
I'm not against mucking around with the mechanic, but I am against making it worthless (such as the subject to the RNG as you describe) or taking it away.
As noted, a key metric for whether a class is "good" in EQ and VG is whether the class is "unique". FD is one of the defining characteristics of the EQ/VG monk.
There's no hint at a monk or SK or necromancer class existing in Pantheon, and if they do exist it's a coin flip if anything like pretending to be dead in an attempt to single out a mob will be part of their repertoire. Dont see this as a crusade againt FD please.
So with this out of the way, would it really be terrible to add resist mechanics? Resists/miss mechanics are fairly widespread in these types of games, so your reaction seems a bit strong. I didnt even suggest the result of a resist but you're not even considering the idea, it's outright bad apparently. You know what, I'm not even expecting a question now after typing this, it's gonna be "because it's bad". I just ask you consider other topics that arent as close to your heart more openly in the future.
That said, new question! Crowd control, how can this be improved upon from the EQ model? Since I only dabbled in VG until level 10 I have no clue about their version(s), any big differences or similar?
Personally, at the very least I would hope for more crowd control classes then EQ featured (2 dedicated and CC skills here and there in others). You had 3 healers, 3 tanks, lots of dps but for CC it was only enchanters and bards (and some people would even argue that, but people are stupid).
I could see a nature or ice twist on CC to allow another class to use the mechanics with different flavors but no other really good ideas. WoW did the "many classes get specialized single CC" which I wasnt really a fan of, and everyone else ran with that of course.