Certain aspects of their jobs absolutely could and perhaps should be privatized.

Getting the patrol aspect of policing privatized would cut down a lot of the worst of the stuff cops get caught doing.

You don't see rent-a-cops going off and killing people.

The inspection and compliance related clerical work that a lot of municipal fire departments do could probably be privatized but I don't see an argument for it like I do with cops since they're less abusive. Nobody ever wrote a song called fuck the fire department.