If the police brutally put down hooliganism, it also invites more hooliganism.
Probably, the right solution involves better policing of police, and throwing out the bad apples. But police culture is very insular, and their labor unions have quite a bit of political power. They protect their own. So, that's easier said than done.
It's quite a catch-22 situation.
I agree with your note about policing the police though, and the difficulties in doing that. Probably trying to reduce the power of police, and its role in society, will be more feasible than trying to get prosecutors to work against their colleagues in the force.