I don’t think an incompetent school nurse would be a bigger problem to me than my child dying.
The bigger problem is how many other children receive substandard care.
In England the protected title is "Registered General Nurse" or "Registered Mental Health Nurse" - a registered nurse is qualified to a certain standard and has a professional registration.
Nurse isn't a protected title, so it's possible a school nurse has minimal qualification and no professional registration.