Beverly was the Starfleet Surgeon General.
No, she wasn't. That would be ridiculous. Given that there are active duty physicians (such as Dalen Quaice,
her own mentor) who have been in practice for decades longer than she had.
The Starfleet Surgeon General is also called the Director of Starfleet Medical,
Only in fan projects. In the
canon, there is Starfleet Medical (the organisation which sets policy and manages medical operations for the fleet, possibly Starfleet Medical Corps or Medical Command, which is controlled
as in reality by the Surgeon General) and Starfleet Medical (the
location, referenced directly at least twice and ambiguously on several occasions when characters talk about something happening "at Starfleet Medical", formally Starfleet Medical Center [San Francisco*], but shortened to Starfleet Medical in the same way that "Operations Center" often becomes "Ops")
so why can't they also be called the Head of Starfleet Medical?
Because the location clearly exists (it was originally the Earth Starfleet Medical Center in the 2150s (known as Starfleet Medical)*), and it having a commander/manager for day-to-day operations separate from the flag officer who commands the entire corps is entirely consistent with RW practice and presents far less
of the issue that you highlighted for Crusher's career.
For 30 years I have never thought that Bev was not the highest officer commanding all the Doctors in Starfleet.
You're not the only one by any means, however IMO this doesn't make sense given the reasons above, and I see no
advantage to assuming that she was promoted to such a lofty position when a far more plausible option exists that equally fits the
evidence.
*Klaang was being treated there by Phlox et al when Archer first encountered him.