Wishful thinking and totally wrong.
The Federal government role in education and healthcare is through the States. The states themselves can determine how much they want or want not to get involved in education and healthcare.
States didn’t have any role in healthcare for much of the early Republic. Just like it didn’t have a role in any other field of work. It used to be a free country.
Now everything is turned into giant corporate cartels, and it makes little difference if their cronies are in DC or the Statehouse, they’re still oligarchs.