This is actually a pretty good idea. Not only could we remove stuff that you mentioned, but we could also remove inappropriate links that people have posted, like in the past. However, deleting individual messages might be a better option. Clearing the entirety of chat would get the job done faster, but that could ruin people's conversations, (which, I guess would probably already be ruined if there's a spammer) however, deleting individual messages would be tedious and could potentially take too long.
As for allowing experts to kick people, I'm not so sure that's a good idea. In the past, Gligurr abused his power as an expert, and, while I'm pretty sure that's the only case of that happening, it could potentially happen again. I'm not sure if this is possible, or how hard it would be for PM to implement, but maybe a system for experts to start a vote to kick a user, and if a certain number or percent of the people currently in chat also vote for the user to be kicked, the user is kicked. There's still potential for that to be abused, but I feel like it would be much harder to do so.