What Brennan needed was meaningful PT running the offense with the first string offense, He wasn't going to get that this season unless Burrow got hurt, He is not going to get it in the remaining games, Wearing a headset wouldn't hurt anything and he just might learn something that will help him next year.
Being in the press box would be beneficial but it's not something that backup QBs ever do on any team and it's not ever going to happen. Headsets cost what? $200, $300 bucks. Give one to all the QBs on the team including the walkons.
Every second stringer's job is to be ready to enter the game at a moment's notice, fully aware of the situation. I don't know how a backup QB could be fully aware of the situation if he is not listening to the OC/QB communications.