From a storytelling perspective, what is the point of her Vulcan background if not to imbue her with Vulcan traits? I don't get it at all. I actually would have found it interesting if, rather than sulking remorsefully, she stood by her actions as the logical thing to do. That would be an interesting conflict, one that could put her at odds with crewmates who can't understand such behavior from a human.
I don’t get the “Why would you expect her to act like a Vulcan?!” Argument.
If somebody goes to China as a little kid, is raised there and go to school there, I would kinda expect them to speak Chinese and know how to use chopsticks when they come back.
If Burnham spend her childhood and school age on Vulcan, it’s hardly unreasonable to expect her to at least partly act like a Vulcan.