Now I know this will be unpopular but it would be true in the sense things would be more difficult and there would be more animosity between healer and people who don't learn mechanics...
Make Raise an ability used only outside of combat.
How many Alliance raids have you been in in which you pull through because the healers are on top of it and just pick people off the ground time and time again? I've seen it a good number of times myself and started to think...
Man...if it wasn't for Raise...this run would have never got as far as it did.
WoW did this and I remember it was hectic but it meant everyone was on their game. If healing was poor...then tank goes down followed by DPS and then healer. If tanking is bad then tank goes down and healer struggles to keep DPS alive. If DPS is lame then the tank and healer expend their resources till dry and then a wipe will happen shortly after.
However Raise is easy to do here. You just dust them off and it's no big deal. Between Thin Air and Lucid Dreaming my WHM may as well have infinite MP.
Fights would definitely change if Raise wasn't a "fix-all" solution readily available.