Even if the royal family wanted to strengthen their interference, the magic school could... move away, to another country, and rebuild the school.
And if all the schools from the Magic Kingdom left, whether or not it could still be called the Magic Kingdom would become a question in need of an answer.
"Since the school is so powerful," Jed mused and enquired, "why does it obey the royal family, instead of just managing the country themselves?"
"They are essentially doing that now," Yasiraqi smiled wryly, "however, there are many contradictions between the magic schools, and it's not easy for them to work together in harmony."
"That has nothing to do with us," Xi Mu said calmly, "We're here in the Magic Kingdom solely to learn magic."
Jed nodded, "Right."
"Hecate is one of the sources of the internal strife," Yasiraqi reminded, then stopped in her tracks.
"Here we are, this is the room I booked." She took out a magic key, unlocked the door, and pushed it open.
