There are certainly people around who put their aircraft onto a Public Transport C of A and then hire it out. I have benefited from two aircraft hired out in this way.
The advantage to them is that they get income to help with the fixed costs plus they get to choose who they let fly their aircraft.
The advantage to me is I get the same availability as a group aircraft (in practice availability is slightly better) so I can take it away for trips, often at short notice. Although I pay more per hour than I would in a group, I don't have to find the capital expenditure, which for a share in an airways-equiped fast tourer is beyond my current means.
You have to keep your eyes and ears open; these opportunities are rarely advertised.