Gotta get in that power harassment/unnecessary sexism/nepotism bullshit beginning to hook the target audience, I guess. Because it's otherwise entirely irrelevant to the rest of the plot once we've established that she's willing to do whatever it takes to save a patient. Mangaka really can't resist hitting all the mandatory checkboxes just because it's the normal thing to do.
How can you say it's irrelevant when you are actually proving it's not? When she's reincarnated into a different world, into an existing role where she's a shunned person (due to lacking magic), obviously she would need to have an aggressive and proactive personality to get anything done and to go against expectations and authority. The backstory merely made it clear that's her character. Of course folks like to see the MC actually get things done (except for the slow life isekai fans), so maybe nobody would complain even without the backstory, but it certainly doesn't hurt either. Furthermore, this is probably far more impactful in Japan than in the West, since Japan is rather hierarchical and tradition-bound, so going against those above you is a bigger deal.
Thanks for the chapter!
inb4 she's in a world where washing your hands is considered blasphemy by their doctors.
If they only heal with magic, maybe not even needing to touch the patient, perhaps it doesn't matter. Kind of like if you are a surgeon using a remote-controlled surgery robot from far away, it doesn't matter if you are clean or not; you'd just be sitting in a room with computers and the operator's equipment for the robot. Sure, you don't want to splash energy drink on the equipment, but you aren't going to infect any patients in person.