This is a really solid point with which I agree! I think the only caveat is there is much debate about where to set the minimum wage, and it's not crystal clea

This is a really solid point with which I agree! I think the only caveat is there is much debate about where to set the minimum wage, and it's not crystal clear what is the appropriate number. So for that debate I do think it is reasonable to use as a proxy "is the employee paid enough to not qualify for means-tested social assistance programs," because there is obviously a relationship in practice between the minimum wage and the amount ultimately spent on social assistance. This is only really true because the means-tested programs phase out as income increases, which would not be true of single-payer healthcare (so the argument doesn't make sense in that case).