If not "crippled by government", schools and hospitals would be Darwinian shitshows that absolutely guaranteed rising health and income inequality.
I agree that things like fast computers are nice side effects of allowing capitalism to go to work in some arenas, but, in others, you definitely need government to reduce the pernicious effect of unadulterated profit motive.
It's appealing to think to yourself "hey, I make pretty good money, why shouldn't I be able to use that to buy a higher-than average education for my kid?" This is fine--hire a tutor. But taking your tax dollars to a for-profit selective academy that most don't have the option of using contributes to the degradation of public schools that you helplessly claim to be an unavoidable consequence of their being government-run.
Institutions meant to serve all only work when everyone contributes to them. Private, unregulated healthcare and education, by design, only serves those with money. Since health and education are, in the long run, how we generate personal wealth, this scheme is sure to accelerate the widening of inequality.