Apparently most cruises in the Med and UK are either limited to cruise line only excursions or no leaving the ship at all. There has been talk that US cruises will have the ship excursion only rule for at least a while upon start up. Nothing has been set in stone at this point though.
I would think that whether or not you can go off on your own will largely depend on the individual countries/ports visited and their local rules.

As much as we love cruising we have decided to hold off until more solid info becomes available. We do have a cruise booked but not until December 2022. If things haven't been set and more normal by then we won't be going.

Things like limiting excursions, wearing masks everywhere except your cabin, having to reserve seats for shows, and other such rules would not make for an enjoyable trip in our opinion.