Wouldn’t a (high enough) UBI mean the free market would create “affordable” education and “affordable” health care and obviate the need for unemployment benefits?
Regulation isn’t the reason those sectors aren’t free markets. On the contrary, regulation exists because they can’t be free markets. Both lead to market failures due to information disparities, principal-agent problems, massive externalities, and a lack of free choice (in the case of health care).
The issue is the amount of regulation, of course. Regulatory capture can have worse effects than most market failures, and healthcare is one of the most obviously "captured" sectors.
I would prefer more regulation to make sure prices are transparent. The current system is set up to make prices as opaque as possible. The employer has a lot of information, the provider has information, the insurance has information, but the patient is being kept in the dark. That is, until the big bill comes in the mail.
No country that has achieved high-quality affordable education and health care for its citizens has done it via market-based means. It probably can't be done.
Money is a representation of wealth, if you print more of it, the money loses it's value to match the wealth. We call this inflation. You cannot give away wealth that you do not have.
If we truly had a free market, we'd have none of these issues, since wealth aggregation wouldn't be prevented through regulations.
For example, you can already get free education of mostly everything from the Internet, but without getting a piece of paper at the end with the stamp of some university. It's a form of regulation, since without that piece of paper you'll have a hard time selling your services. Similarly, you can get all the information you need to lead a healthy life style, making it less likely for you to even need health care. But still lots of people just eat till obesity ruining their own bodies. In Japan there's a system where your company does yearly health checks and if you gain weight, you have to pay more in taxes or some such scheme. Curiously nearly nobody in Japan is obese.
... so you know... obesity isn’t usually from eating to excess because you can. It’s from eating high calorie low nutrition foods. Poor people in the US aren’t obese because they have excess it’s because it is cheapest to buy high calorie foods. Obviously I’m not talking 400lbs, that still takes effort and money, but 250lbs is easy to hit when poor.