I've flown across Europe extensively on *A and ST carriers since the Light fares were introduced, almost always in Y.

Yes, it is already a problem with the first bag. Yes, elites get a free bag always (on AFKL and ST in general, *A is more difficult). No, this doesn't help much. Elites take a carry-on because they want to grab it and go, not wait until it comes out (on occasion, I had to wait over 20 minutes for a priority bag on some airports).

The solution would be to proactively arrange gate checks even before boarding. Those who can afford the wait can then check their carry-on without slowing down others. I've seen it happen once or twice, went quite well.