I don't think this is nearly the problem you perceive it to be. If I'm in public, I chose to be there.
And for the record, I'm a huge fan of police bodycams.
David Brin has a book about surveillance society - which unfortunately, I never finished reading. But I did get to the part where he makes the point (and I agree with him), that it would be nice if all these cameras were publicly accessible and all accesses were published.
So your daughter goes to play in the park. You access the park cameras, to keep an eye on your daughter. That you accessed the camera should be a matter of public record. If the police have a constant feed on the park, that should be a matter of public record too. If some perv is watching the children in the park, there should be a record of that too.
I'm not terribly worried about the fact of the recording; but I'd like to see more accountability in who does the watching. For police bodycams, I'd like to see more accountability when the office turns the thing off; perhaps having to key some sort of code that says why the camera is being turned off.