Think about it this way: having bodyguard is a luxury, just like gourmet food or high-class fashion. If she want to eat gourmet food 3 meals a day, make enough money to afford it -- if she want 24/7 bodyguard service, also pay for it herself.
Having bodyguard is in no way a luxury, it's a necessity for anyone in a high position, especially a child.
Unless the school is able to provide an equal security, stopping someone like a saint from having bodyguards, is a danger to not just her safety, but also everyone around her, since it would embolden any idiot, dumb enough to do something, since now she is unprotected.
A rule like this, not only serves to give the kids a worse education since they are now busy having to deal with a job too, while trying to learn, but also stops any high ranking nobles like the prince from taking the top class, because of the risk of getting assassinated, all ending with dumber people in power then need be.
And all this could be avoid by simply, allowing other to pay for bodyguards, and allowing anyone who choses to start lower, to advance at a later year.