An FC can easily be run like a dictatorship if desired anyway. Forcing someone to shut up just because you want, or else face gkick.
And although I've been fortunate enough never truly to run into a situation yet in which I felt muting a played in my FC would be required, although at times the urge did come close. I have encountered such scenarios in prior games. And often it's not so much a matter of muting because an officer wouldn't want to talk to them in such a scenario. But either because:
A) Two members are going at it against each other. Often over the most pointless thing. Where the urge came close was a recent example, a few members selling wedding bands whereas one person strongly opposed this concept. Things were turning heated for a moment. However, the level of discussion fortunately enough was maintained relatively mature. A few years ago I remember a heated argument between two guild members in WoW though over the game's shabby performance in Wine. A windows user told him to just suck up his love for linux and dualboot to play WoW. Things escalated quickly. The usual "will figure out where you live, and <fill in random threat>" lines were reached within mere minutes. Despite trying to get them to shut the hell up they kept going at it. So I gkicked both. Ultimately one ended up showing remorse for his manners, and got an invite back into the guild.
If there'd be some form of moderation available however, it'd be a lot easier to not have such a talk escalate to such levels. Not for the sake of being a dictatorial ruler over one's own guild reigning down upon your own members, but rather to protect them. From the need of being removed (temporarily) out of the guild. But also from risk of infraction (as yes, GM's do ban for what is said in private FC channels if someone reports it).
B) To quickly temporarily block spoilers. Sometimes excitement can go high, detailing about the plot of the latest blockbuster seen on opening night. Easily forgetting others are still to see it as well. A quick mute, followed by some chat to inform them to please stop spoiling, unmute can go a long way. Now often there's still another line of spoilers coming in, just because it's being typed as you're typing yourself.