[DINKDINK]

>To have a centralized state sponsored education or health care system allows it to be more efficient that smaller for profit institutions that have incentives to increase cost to the students as their profit depends on that.

An institution whose survival depends on profits is incentivized to...reduce costs, not increase them. All profits are, are the difference between what is consumed and what is produced. Either your argument is: institutions who produce more than they consume are bad or a service provider ("centralized state education") can be granted a monopoly to the service and will, more efficiently, produce the service. Typically monopolies charge monopoly prices (bad for everyone except the monopolist), if the granted monopoly has its prices legislated to address these concerns (the case in Europe), it must sacrifice either on {cost, quality, quantity, quickness of delivery} of the product.

If you really do think that monopolized industries outperform markets with "wasteful profits" you might study the history of the CCCP and democratic welfare states.

The market manipulation that started in US education is a result of price fixing -- the price of education is a molested price: service purchasers don't select on electing a provider based on cost because that market price has been pushed up by government-secured debt to which a party cannot default on (otherwise know as selling yourself into slavery). Since producers have less competition on price, they compete on quality, quantity, and quickness. It's the same issue that resulted in the FAA price-setting airline tickets - airlines couldn't compete on cost so they had an ever increase set of luxury options to attract customers.

See:

https://en.wikipedia.org/wiki/Airline_deregulation#Civil_Aer...

https://fee.org/articles/the-effects-of-airline-regulation/