It's not just that nobody likes to miss, it's that missing can have pretty far reaching effects. Miss your aggro combo as tank at the start and watch the BLM be gutted despite quelling strikes. A missed autoattack does not do much, but miss a trick attack and you just cost your group 10% DPS for the next 10 seconds. Not to mention it might cost you Enochian or Greased Lightning if the timer is tight - even if the chance is low, it can lead to a pretty big DPS loss.

I can tell you right off the bat, if skill effects still applied if the ability "missed", 100% accuracy would quickly become a lot less mandatory. It would still be capped however because it would still offer the highest return up until the cap - and none after, as you have already said yourself.
It's also a bit awkward that it really only matters in EX/Savage content but even casual equipment is loaded with it.

Personally, I don't find the stat particularly good or interesting and could well do away with it - but frankly, I think every secondary stat that doesn't change your playstyle could well be done away with and if we would scratch every stat that doesn't change gameplay, we would only have two stats left:"Power" for progression and "Speed" for gameplay. At that point, you'd really have to brainstorm new ones, because it's fairly obvious that two stats are a "tad" meager.