> Calling public schools a welfare program disproportionately allocated to the poor seems like a stretch too.

It's not he's saying. He's saying that public schools should be considered part of the "welfare program". Which they probably should since public schools, like social security, are program that benefit society as a whole, which you can (or cannot) use depending on your personal situation.

Someone else notes that those program tend, on average, to mostly benefit poor people - which they probably should. But it's not systematic.

So I don't really see any taxonomy issues here.

Medicare requires having paid into it for at least 10 years, and I believe there is some convoluted means testing going on with all the different “Parts” of Medicare and how much one’s premiums and benefits are.

Social security is similar, see my other comment.

There are varying degrees of means testing and wealth transfers happening with Social Security, seen when the government changes the age one starts receiving benefits and the amount of the benefit (and which cost of living adjustment to use). It is not a cut and dry case of social welfare, but it is also not a “what you get is what you put in” program either. I think it will only become more and more means tested and more akin to a social welfare program though.

By that logic universal healthcare isn’t a social program either, it’s government mandated health insurance.