Nope, we don't even nominate the exits anymore. We did in past airlines but that is left to the CC to determine these days.
Spruce, please tell me you are joking.
I am very pro-CC and treat them with the ultimate of respect for the very difficult job they do day-in day-out. However their situational awareness leaves a lot to be desired in most normal situations - made much worse by a tiny cabin window they have to look out of in terms of emergencies.
Surely you have the bigger picture when it comes to evacuation?: Engines on fire, prevailing winds blowing said fire in direction of evacuees, live runway/ taxiway on a specific side of the aircraft, a known spillage on one side that the CC would have no way of knowing etc.
The above are just a few things I can think of as to why CC should never be given the authority to decide what side an evacuation should be made on.
Of course in the event of no communication between flight deck and cabin due to a catastrophic failure, then obviously CC need to make that decision.
Also regardless of what the Captain says, CC should always do their usual checks before they open their respective exit.