That's one thing that does suck about us sound guys. RTA and room anaysis is a noisy task. Fortunately, there are a large amount of tools that can speed that up tremendously.
I personally like to keep the stage absolutely quiet whenever possible for the lighting guys to get their communication done, which may often be via shouting. You got the guy at the desk, then you've got a production manager on the floor, and then at least another guy or two up on the trusses aiming and focussing. I want them to have the best chance of communication for their safety.
As long as I can run my RTA before lighting has to do that task, or afterwards(and well before the show), I'm happy. It typically only takes me 5 minutes or less to run my RTA. Since I have rooms I frequent often, I have settings saved, which is a time saver.
In my case, it's "load in, do the show, load out" in the same day. Rarely do I get advance time to work.