Or importantly take an interest in the quality of the government education ministry.

That's one of the big dangers of allowing private services to move into the place of public goods. The most powerful and influential people are allowed to shield themselves from the consequences of their bad decisions and political allegiances.

I've often thought it should be forbidden for politicians to send their kids to private schools, or for them to live in gated communities and hire private security forces. I think they're reasonable arguments to extend this to very rich people also.