I'd imagine it would be the same as with any boss fight where DPS need to volunteer for mechanics/tasks, and they are all suddenly quite, waiting for another DPS to sign up.
Which is, someone else assigns them the job, and they try to do it anyways.
It's possible they might leave the group, but I personally don't think they would.

Over all, communication should always be the goal of the game. Not turning our brains off, and watching netflix as we play.
So I would see a few people afraid to do it, but after they see all responsibility pretty much goes to the tank using CDs, and the healer keeping them up, they wont be as nervous, and no longer be an issue after a few days of such a job being released. (Which wouldnt happen anyways. More of a fun idea.)

As for the caster thing, I forgot a part about lowering cast times on AoEs. I still need to make another adjustment about the stance I forgot about as well.