Is the concept of a 'Federation Doctor' feasible?

[Deks]

It's entirely possible that in Trek, humanity's methods of learning are much more advanced compared to our own.
Repetition is NOT an effective means of learning.
There are even classes today that help people make a mind map of sorts which helps to improve memory, then also for speed reading, etc... and for a lot of people they work.
It's possible Trek humans developed their own modified/more efficient versions of these programs that help children and adults with learning.

Hence they basically approach eidetic memory capabilities via training, and adults have a tendency to retain a lot of the childlike abilities for memorizing things.

Vulcans for example have a better than average (today's humans average) memory.
That's probably thanks to a large degree of their mental control techniques and meditation (both of which can improve memory functions in the real world as well).

Take your picks.
The brain can hold vast amount of information... and also, there's one more thing to take into account.
Federation doctors would likely have a 'base' form to work with (humans or their own respective races, most of which are shaped in a same/similar fashion) and then expand on the variations that other races developed as a result of their evolutionary process.
The intricate details would be in the internal functions of the body which would probably differ from species to species, from the mildest variation to the most extreme.

And then there's the vast computer database for consultation.

Plus, one thing to not forget is that these people have a tendency to study about things that they actually ENJOY.
They aren't forced into a line of work that won't be connected to their desired profession or field of interest... and since humans do have a tendency to memorize things they are interested in, the Trek humans would essentially be VERY good at it.

 

[7thsealord]

It has become well-known that, for many medical procedures, children cannot treated as if they are simply under-sized adults. Tolerances and the like are quite different. So, we have pediatrics as a medical speciality - one of a great many specializations that can be found.

Theoretically, specialist Doctors would be able to handle the fundamentals of medicine. But that might also depend on how much in practice their respective specialities allow them to be. So, a doctor who spends twenty-plus years studying (for example) ear ailments may not necessarily be fully up-to-date on .... I dunno, dealing with an ingrown toenail?

No fault of that doctor, medicine is a very complex field, and keeping up with EVERYTHING that goes on is probably impossible unless you do absolutely nothing else with your time. Trekverse doctors undoubtedly have all sorts of assistance and advantages , but I suspect that even they would tend to specialize.

Then too, the similarities of many humanoid forms would be undoubtedly be helpful for pratitioners trying to cope with a bunch of alien races. One may argue about these similarities, but consider how easy it is for some of these races to cross-breed with absolutely minimal medical intervention (Klingons and Romulans, for example). This suggests that the similarities of certain races can be quite major, which would make an interspecies doctor's work easier. Sometimes..

 

[Newton]

The computer may play a large role in assisting doctors.

Dr Crusher loved waving her medical tricorder around. That info is probably transferred straight to the computer which, knowing what the 'normal' levels are for a particular species, can easily let the doctor know if anything is amiss. That, combined with research on an extensive medical database may be enough to successfully treat other species.

Also, assuming that most humanoid species in the Trekverse are fundamentally similar, as established in "The Chase" (TNG), most treatments would likely be similar, with only minor variations between species. Sure, there have been cases where the doctor couldn't treat a particular species because they did not know the physiology well enough, but this seems to be relatively rare.