Even people with money don't go for regular medical checkups until their health forces them to. So while I agree with what you say in most cases, in this case I think giving poor the money would predictably result in zero of them going for preventive tests.

Some amount of "paternalism" is good for society. Someone likened health to car maintenance, but I can tell you that of the drivers I know, zero of them would get their car the yearly technical check unless it was explicitly illegal to drive that car otherwise. I'm starting to believe we should have something similar in places with public healthcare - there should be a set of free, mandatory, noninvasive checkups to screen for diseases that don't have symptoms noticeable by patients, and there should be a way to compel everyone to take those tests. It would be better for everyone's well-being, would save public healthcare a lot of money, and the doctors could stop attaching unrelated tests to getting prescriptions for glasses or birth control.

The way to do it that respects freedoms would be through incentives. E.g. if preventative checks would save public healthcare a lot of money, then give people that do it tax credits or literally pay them money to do it!

With cars, there are greater third-party effects (i.e. your car failing and crashing into someone else), so it makes sense to require a certificate before one is allowed to use public roads.

Agreed. And even with cars, you could internalize those externalities with big taxes. (But I guess, if the externalities are big enough, that big tax amounts to a fine or even jail.)

Poor person on disability here. Medicare in the United States gives zero dollars for eye exams and glasses, so good on Australia for actually caring about their needy. The process of losing nearly everything I owned due to my work-acquired disability and trying to navigate the confusing and mentally arduous process of getting benefits has been every bit as bad as the disability itself. Getting benefits is so confusing that I normally just don't bother. I for one would much rather receive an eye exam and prescription instead of yet another confusing bureaucratic layer between myself and my health disguised as a "choice". I would also assume that whatever stipend the government would come up with, it would pale in value to the cost of the actual procedures involved. And thank you ajnin for speaking up for us.

My suggestion was not to add a bureaucratic layer, but to just hand out the cost of the procedure in cash with no questions asked.

Of course, in practice the government would probably come up with silly layers and restrictions on how to use the money etc.