It's easy to talk about 'not introducing competition' from your armchair. It's way harder when it's your children not getting the education and childhood they deserve; and it's not just about education itself, actually IMHO (from my personal experience) it's mostly not about the education but rather about the environment at the school; I won't send my children to a public school not because of low quality teaching, but because of bullying (both by other kids and by the teachers) which the institution was unable to solve for decades or maybe even hundreds of years, and because I absolutely don't believe in exams, preparations for exams, and marks, and because I have zero control over public schools as a parent. Even a high quality school with the classic subjects/preparations/exams/marks system still would be a reason to move to a freer country to me if I lived in Finland, and in fact I have a coworker here in Prague that did just that.
Even the richest person on Earth can't fix the public schools with their whole fortune, not even a group of the top 10 could - they wouldn't be able to provide funds for more than a year. And private education is definitely not reserved to the rich, I don't think the majority of parents that send their kids to private schools have more than average income.