I think it would be a reasonable definition of "social problem" that it requires two people to have it, and that they must have it in relation to each other, which is to say, some sort of social interaction or communication must be involved as well.
Sanitation is a problem for one person as well, as is health. Social problems arise specifically with the interaction of two people. You can't have a scam without two people, for instance.
Definitions that collapse the entire space under discussion into one category are useless. If sanitation is a "social problem" then everything is a social problem, and the reason why that is useless is just that a definition that does not distinguish has no utility. In mathematical terms, to say that something conforms to that definition yields zero bits of information. "Public health" is its own category. In the real world no two categories can ever be fully separated from each other but just because plausible scenarios can be spun out in which sanitation becomes involved in a social problem doesn't mean that on the whole it is much better understood and talked about as a separate category.
Crypto has social problems. If one person sits in a basement and "does crypto" by themselves who cares? They can declare they own as many basement-coin as they like. It takes a second person to have a problem.
The original post said plumbing, not sanitation in general. Plumbing mostly solves a problem that arises when you have large groups of people. An individual or a small tribe can keep the waste and drinking waters separate by walking downstream a bit.
I agree with you on the uselessness of definitions that don't distinguish anything, and I think your conceptualisation of a social problem as being something that requires multiple people to interact (like a scam) is useful, admits a very clean boundary, and deserves a name. I would call such a problem a purely social problem. But I think there is a broader concept of "social problem" that makes sense too, even though it lacks such sharp edges.
I think it's reasonable to say that a problem is a social problem to the degree that its severity as experienced by one person depends on other people's behaviour.
If I accidentally drop a rock on my own foot, this seems to be obviously not a social problem. But if I am more likely to be carrying a rock in the first place, or less likely to be wearing protective shoes, because of how society is organised, then to that extent I claim that it is a social problem. This is not an abstract example: Over time, changes in society's attitudes to dangerous kinds of work have directly, and indirectly through health and safety legislation, led to massive reductions in workplace harm since the Industrial Revolution.
Under this rubric, all it takes for a problem to be social is for it to be possible to imagine that society being organised differently would lead to a different level of suffering. Does this lead to nearly all problems being classified as social problems? Yes -- but that is not a problem in itself, that is just an accurate picture of reality! It is still useful -- indeed much more useful -- to place problems on a spectrum of social-ness; nothing "collapses" unless we are determined to make a black-and-white distinction.
Sanitation is a problem for one person as well, as is health. Social problems arise specifically with the interaction of two people. You can't have a scam without two people, for instance.
Definitions that collapse the entire space under discussion into one category are useless. If sanitation is a "social problem" then everything is a social problem, and the reason why that is useless is just that a definition that does not distinguish has no utility. In mathematical terms, to say that something conforms to that definition yields zero bits of information. "Public health" is its own category. In the real world no two categories can ever be fully separated from each other but just because plausible scenarios can be spun out in which sanitation becomes involved in a social problem doesn't mean that on the whole it is much better understood and talked about as a separate category.
Crypto has social problems. If one person sits in a basement and "does crypto" by themselves who cares? They can declare they own as many basement-coin as they like. It takes a second person to have a problem.