Personally, I prefer it signaled and not entered. Reffing, I typically end up half-hearting the signal (some kind of a flag point with coach eye contact, rather than an aggressive wave). It's subconscious, but recently a few of coaches that know me have noted it's a nice 'this might be coming your way' warning. I like the signal approach as a coach myself, but fortunately in my case a 'signal' from one of you guys can be a grimace or hitting the radio button.

My druthers resolution? Have an official signal and/or a button (because we all so love buttons) that calls it up on the projector. I prefer the former, but I could see the latter for the crowd. Make it a driver's meeting topic.
I can't believe I've never talked about this before. This is why Carol rocks.
First, I look forward to any analysis you do decide on. You've clearly got a very strong handle on the complexity of the question, and you have my apologies as I feel like I've been unintentionally adversarial about it.
Queen City - Queen City was the same week a 2nd of 3 ref gigs, and while I would've loved more refs, we were never toggling screens if we were a scoring ref. (Actually, I never did this, thouh at NYC we had
8 refs.) If I was a foul ref, I'd sit on the possession screen to cross-check, and only flip to the foul screen after I'd signaled one and was otherwise clear--no robots in my zone of responsibility, and my cycle either had all 3 assists already or at least wasn't about to end. Otherwise, we'd radio for entry. I had a truss ref come over and punch fouls for one or both of us a couple times. How was it done a QC? Different places I reffed or played under had better ideas for different tasks, but there didn't seem to be a lot of cross-event consistency even in logistics.
Pedestal - yes, there were a lot of things that worried me about the rules on kickoff (and since), but they seemed to have trade-offs. The pedestal on Kickoff Sunday was my first 'what the heck is the point of that?' moment. The trashcan's only purpose in this game was to make coaches mad at refs, make refs feel bad, upset the audience, raise the responsibility and failure rate of field reset, induce replays, slow down game play, and make dead balls suck more for all parties.
So, in retrospect it actually had a pretty expansive purpose. If I never have to spend hundreds of dollars staring at an unlit trashcan again, it'll be too soon.
Yes, I would presume that this is true of any game. (It's why I keep scores in my head--not that that helped with the Towers, but it did for 2013.) Unfortunately I can't think of any quantitative dataset that would allow us to check things like this, so I've tried to shift my anecdotal assessment at least from 'did I hate this?' to 'how many did I see?'