Lt. Uhura-Brown wrote:
A Starfleet captain who knows nothing about the culture of their fellow Federation co-founders is bad enough, but a Starfleet doctor who knows nothing about Vulcan physiology despite having a half-Vulcan crew member is just ridiculous.
Your problem is you're trying to evaluate the original Star Trek
in light of what later Treks became rather than by what it actually was.
Later Treks have developed a Trek history that says Vulcans were very involved in Earth's first "baby steps" into space and were ubiquitous (and overbearing) on Earth through much of that time.
In TOS, Spock, as an alien serving on an "Earth ship," was a real rarity, and the Vulcans were a mysterious and rather secretive species.
EDIT: I see Admiral Buzzkill
made the same points while I was composing this post.