Techically speaking the commander of any vessel is called the Captain ! :D
I also agree with Sea Tyger's point.. They would Brevet officers they thought were suibtable, because a) they were short on experienced officers b) they were building ships faster than they could crew them c) in times of war it can be a very quick way to rapidly get promoted!
A Brevet command means they can take it frrom you, but hey at least you get it on your service record.
I suspect Captains and Admirals comandeer whatever they feel like taking. Admiral Ross had the USS belerephon, a 'mere' Intrepid (which are really a quite powerrful ship for their size), most likelly because it was among the fastest ships in the fleet, to get round quickly, Ditto the Defiant.. It's easy to say a Captain or an Admiral would have a Sovereign or Galaxy, but there were few of either.. the reason there were a few more galaxy's in the fleet was because Starfleet utrned it's backlog of galaxy spare parts into real ships, to make use of them, but then didn't fill them full of crew.. they were not fully completed ships. They tended to focus on the midsized ships, because they are an order of magnitude less complex to build!
And remember the Sovereign was a more powerful ship, but it is most definatelly SMALLER than a galaxy, it's just longer.. it has WAY less internal volume!