The Making of Star Trek makes it sound like starships do report to star base commanders:
The Enterprise operates at the outer end of a chain-of-command. Immediate higher headquarters is Star Base Command. There are seventeen star bases scattered across the small known portion of the galaxy. Star bases, commanded by an officer with the rank of commodore, provide repair and resupply facilities, replacement of personnel, and so forth. Next higher authority is Star Fleet Command, operating from a central point in the explored portion of the galaxy. Under normal conditions, the Enterprise operates far away and virtually out of touch with higher authority.
This fits with the late 1800s "overseas empire" model which is frequently reflected in TOS. Naval vessels were deployed all over the world, reporting to regional station commanders, a flag officer usually based in some port. It was only with the emergence of the serious German naval threat in the early 1900s that Britain decided to concentrate the navy in strong battle fleets nearer to home, and not without major controversy.
What we actually see of the Enterprise's five year mission is that her time is often spent on fairly routine duties, and she is rarely out of contact with higher command. This seems consistent with a regionally-assigned vessel, though it also sounds like she might hand off from one starbase jurisdiction to another (what the US Navy calls INCHOP or OUTCHOP, CHange of OPerational command).
The four-ship force in The Ultimate Computer may be practicing a standard war deployment, though it does raise the question of how quickly it could be assembled if the starships are normally scattered all over space.
TMoST also makes it sound like there are "only twelve" starships, period. Everything else Starfleet has is smaller. That does sound a little too small-scale to me. We do know there is a dreadnought by TMP, though!