There's a big difference between "for everything you do in public, at least one person witnesses it, but any one person only sees you for a short while" and "for everything you do in public, a specific person is aggregating that information".
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.
But they're not using cameras in the same way. The cameras are always there. If police followed you 24/7 without sufficient justification you could sue for harassment. You have no recourse against the cameras.
I'm not sure about that harrasment question; the case against the long-term embedded undercover police in the environmental direct action movement is still ongoing, I think.