Not one single person I personally know turns them off. What's the point of that? Low end computer or being in a giant hurry?
I used to play with animations, but there's a bug in Windows 7 or Civ VI that causes the leader animations to eat through my computer's memory in no time. The game is unplayable now unless I turn animations off. I wish I knew why. I very much miss having the animations!

Anyway, I'm hoping for a patch today. I just finished my latest game and I'm hesitant to start a new one and have the patch ruin it.