No it should not be that way. Doctors are meant to do more medicine than a nurse. To be fair I think it is just a way the show ends up writing poor and bad female characters.
They think if they make a female character who knows better than everybody and can do jobs that is clearly beyond their job specification and description, that this is how you empower women. I think it is wrong. Also it is not realistic.
for a show that likes to rip off buffy the vampire slayer, could they not have used Buffy herself as an example. What Chapel is in SNW will be the equivalent of Buffy having more knowledge than Angel and Spike (vampires who have lived for centuries, while Buffy is only 17 years) and also knowing more than her watcher, who is meant to teach and guide her.
Streaming trek since discovery have had a history of overpowering their female characters in terms of abilities. I mean Batel is literally a god in the final season, Michael and her mum were the Red Angel in Discovery, even SNW Uhura in season 1 said she could speak some languages that in TOS showed not to be the case.
This is not how you write good female characters. I am sorry but it is not.