I assume the sheriff would be totally fine with putting up signs in that area saying "audio and video recording in progress" then right? That would somewhat address the issue, and should be entirely uncontroversial to both sides.
It's so fundamentally terrifying that someone would consider that "totally fine".
Prosecutors will take breaks in their offices within the same building while the defense has to leave the building in order to have a private conversation, that sounds totally fair and reasonable.
The whole point of contention is that one of the spaces is, effectively, the only convenient places to have a quick, heretofore private, conversation. No one is confused over where the things are.
There is an asymmetric impact to the defense. In our adversarial legal system, we must not disadvantage one of the sides unilaterally.
That doesn't sound like a good compromise at all. First practically speaking, you can't just leave the court building to discuss with your client if they're in chains, and it's super inconvenient based on the layout of many courts. Second, this becomes the excuse for adding audio and video surveillance everywhere, with the excuse that you know about it, so it's okay. Third, considering audio can pick up things like jokes, irrational things said in anger, or just one's mumblings to oneself, it very quickly becomes the excuse to haul in anyone you don't like by misconstruing their words. The fact that it was brought by law enforcement tells you they are looking to use it against people.