I don't have any problem with admirals commanding starships. It suited the story of TMP (and Khan) to have the rank associated with deskjob duty, but it doesn't necessarily mean every admiral HAS to be relegated purely to deskjob duty.
The idea was that Kirk was a victim of his own reputation and the powers that be wanted him to pump out cadets in his own image. Other captains that rose up to the admiralty might have been allowed a more active role than that, because you can only have one person in Kirk's capacity.
One thing Gene wanted to do in TOS was flatten out the org chart. That's why there's no ranking braid for ensign. We also never saw a lt. jg. in TOS although I think the single dashed braid is canon.
The admiralty in Star Trek wasn't shown that often because it made Starfleet feel too bureaucratic. It suits the universe for the higher-ups to be more active. It's boring to watch orders cascade their way down through the chain of command.
The captain going on away missions is something that wouldn't happen in the real world, for instance, and the attempt to address that with a stronger first-officer in TNG failed. Picard was supposed to lead more from the conn. Frakes was supposed to be the swashbuckler. However, since Patrick Stewart had more charisma, he wound up going down to the planet surface as much as Kirk.