True, a rate change is not actually broadcast, but on a PC you can see the rate below the video window/frame/whatever.
I expect that it would change in real time, however if it was changed immediately before the private show began you would have to be looking at that part of the screen to notice, in the brief time it would be there, before the private show started.
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But I agree that, to me, a public negotiation and rate change is not a good look, but... "her room, her rules" ?