The police can already do the latter by having officers follow you. As long as we're talking about individuals, I don't have a problem with letting them use cameras in the same way.
The real thing we object to is dragnet surveillance, and we should think about how we limit police power accordingly. It might be the case that there's no effective way to prevent abuse of cameras in this way, and the only thing we can do is remove them. But if we reach that conclusion, it should be argued from principles, not kneejerk objection to cameras.