Earlier quoted context omitted.
Agreed. I think it's simple common courtesy that the person extending the invite picks up the check.
In my experience, that's culturally exclusive to the upper-middle and upper echelons of society. In working class groups, no single person is expected to pay for everything; it's split relatively evenly.
Outside of my family, I've also had friends from relatively poor backgrounds insist on paying for lunch or drinks before. And I've had wealthy friends act extremely petty down to the penny. So overall I've found it's hard or impossible to generalize too much.