Even just reducing traffic, noise and pollution is a pro.

You can't reduce the demand for going to work or shopping for groceries. Arguably the real problem is we've put too much in too small a space.

No, but it does help incentivize people to do those things using transit, or at non-rush hours and gives less traffic to everyone else.

It doesn't work if there aren't alternatives, of course. But NY and London do have them.

I can not imagine there is a statistically relevant number of people that travel to Manhattan to specifically to grocery shop.

NYC has the best public transit in the country, and they spend a lot on it. It's one of the few places in North America where congestion pricing could even work.