I’ve often thought that would be very helpful too!
You might find it possible to use Discourse Dynamic Groups to achieve this; I’m not sure if it can be configured to detect who is the owner of a group at present, though.
While it would not reduce the group number nor simplify the initial config of each private category, it would mean that the groups of moderator/owners would not need to be actively maintained (which I’m guessing is your main pain point).