For the “why do people care” comments - he will be our King, our head of state. His level of education, the sort of people who he has been surrounded by, educated by, the sorts of ideas and ideologies he’s been exposed to - this all matters because he will be our Head of state.
School and education shapes the boy to a man, and in cases with boarding schools, the school ethos has a much bigger impact than day schools in what sort of adult he will be.
This is the price his family pays for their privilege and power- they and their dcs don’t get the same level of privacy as normal people. George’s future exam results, his sexuality, his politics, his choice of romantic partner(s) matter, because he will be our king.
And because being friends with the King/future King is known to be advantageous politically and financially, which school he goes to and who gets to be his classmates is going to be of interest to parents who are hoping to give that advantage to their children.