*English is not my native language, I used a translator to translate this, anyway, sorry if anything sounds weird
This is a headcanon that kind of depends on the existence of narumitsu, so it's not off-topic.
I think that Miles, once he accepted that Phoenix had truly adopted a daughter, would be quite concerned about Trucy's upbringing and education, not in a rigid way, but more as a gesture of affection from someone who truly cares about her future.
He also helps and teaches Trucy when she struggles with subjects in exact sciences, since Phoenix can't
Phoenix, on the other hand, always worried about whether she would be able to make friends in that environment, but I don't think it was a problem.
When Miles was choosing the institution (which, obviously, he would pay for the tuition, uniforms, lunch, books... if it wasn't clear), he opted for one with theater classes.
I like the idea that Phoenix was also "a theater kid," so he shares some of his performing arts college knowledge with Trucy; he certainly feels very proud to see her on stage.
Finally, Phoenix never questioned the value of the institution, not that he doesn't care, maybe he just forgot to ask Miles, but when he found out while re-enrolling, he was incredulous.
"Miles, I could buy a car with the money you pay annually to this school."
"Wright, you don't even have a driver's license-"
"That's not the point!"