I've generally been on the "Rusty will get to stick around" side, but I definitely think that if Rusty is removed, Tommy is the one who will replace him.
In fact, one thing that occurs to me is that if Rusty were forced to step down over the Cathy cluck, it might be a good motivation for the MC (and others) to finally start trying to work out just what happened. If they can find evidence someone else hacked their account to post the cluck, they might be able to get Rusty reinstated and end Tommy's reign of terror.
Otherwise, if Rusty is allowed to remain, it's not clear if they would have any motivation to solve the case. And it seems highly unlikely they could crack it between the end of Episode 5 and the meeting on Monday morning. So having Tommy take over "for now" could be a good way to advance the story without ignoring old plot hooks or trying to cram everything into a single night (again).
As for Tommy himself, the guy is clearly a jerk, but it's possible there are less negative sides to him, too. Hopefully we will find out before we are faced with the opportunity to punch him.