I think that is a good question in general for any series. I mean why is Ogawa just a nurse? Shouldn't every person on the Enterprise medical staff be a fully trained doctor? Sure there's a need for a nurse's role, but I'm guessing other doctors would be able to do the job just fine while also being able to act as the person holding the scalpel (or 24th century equivalent).
I can understand what you're trying to say there, but I'd actually suggest that you've mostly got that the wrong way around.
Let's look at the four known medical staff on NCC-1701:
Leonard H. McCoy - described as Ship's
Surgeon at least as often as he's described Chief Medical Officer. Likely therefore primarily responsible for "invasive" medical procedures, also leads in diagnostics and research.
M'Benga - expert in xeno-medicine, specifically Vulcans and a capable general practioner.
Sanchez - pathologist, likely also assistant surgeon.
Christine Chapel - assigned as a nurse, also a trained medical researcher (by implication specifically in medical archeology (palaeontology?), some knowledge of pharmacology) and a capable surgical assistant, educator, paediatric care specialist/child psychologist.
IMO, it's reasonably likely that all four of the above have
doctorates and as far as 'general practice' (treatment of known illnesses and injuries with established cures, promotion of general health and wellbeing) I would bet that Chapel is
at least as capable of carrying out treatment as any of the others, and probably more than Dr Sanchez if he (?) is specifically a pathologist.
Where IMO the role of the medical doctor ("physician" or "surgeon") comes in is dealing with the
unknown and coming up with
new treatments (not that nurses aren't part of this process, they are, but the MDs are
leaders in this).