I think they should be allowed to point it at places inside their store, with prominent disclosure to people entering.

I don't think they should be allowed to point it at the public sidewalk.

> Should they not be allowed to do that?

If that camera system is closed-circuit and its data is restricted to the premises they should be permitted to do that.

If the data from that camera system [0] can be removed from the premises by anything less than a search warrant or court order, then no, they should not be permitted to do that.

I know this isn't how the relevant laws work now, but they haven't been adequately updated to account for radical changes in the ability for companies to perform mass surveillance.

[0] ...whether raw or "processed" by -say- a "customer analytics" software... [1]

[1] Want a count of the day's customers? Check register receipts. Want to know what displays are most popular? Ask your employees, or employ someone to take notes. etc, etc, etc.

Try walking around a grocery store with your phone and take a picture of every person you pass. See how they react.

That's the expectation people have for privacy.