As any operator, half-op, or even regular site user can tell you, people love to peanut gallery in #site17 during ban appeals. Even when people want to butt in with relevant material, it is of exactly zero positive value and only make the presiding operator's job harder.
So my proposal is simple: chat operators should be able to, at their discretion, voice the user appealing and mute #site17 for the duration of the appeal. The #site17 chat topic will be appended with "If channel mode is set to +m, please PM an operator for help". If at least two other operators feel a mute is unnecessary, they can undo it.
I do not anticipate this being used regularly; most likely it will only see use for cases where users are appealing situations like pronoun-bot-abuse or misgendering, which tend to be rife with other users trying to offer their two cents. If a majority of ops concur with this proposal, then we will implement it as soon as a majority is reached.