This is not a peeve really, just an opportunity for me to learn how atc works.
A lot of my flying is on the fringes of the NAS with little traffic it seems, and I often key up to talk to a center controller who has turned off his mic for my part of his sector. So he hears me, but I cannot hear him or the other pilots he is talking to.
(Be assured I always listen in for a lengthy period to ensure I am not talking over someone.)
So I call up center and immediately, atc switches on their mic for my sector - I can hear a pause, followed by part of his instruction to another a/c. (I cannot hear the other pilot as all that is taking place on another frequency.)
The main issue is that I don't want to be walking on anyone, least of all atc.
So, in my mind, if he left his mic on for my part of his sector, I would hear him talking to other pilots even if they are on another frequency, and would not fill his ears at an inopportune time.
Why does that mic get turned off? I'm sure there is a good reason.