Fundamentally, there is no difference between making John pay for his dad’s bills, and making John pay for a complete stranger’s bills.
This is the philosophical or moral view I'm referring to, yes. It's a subject on which the Constitution is agnostic, although if these were federal laws, sure, some kind of argument could probably be made. Someone like William Rehnquist would be likeliest to have made it, though.
Do you believe it would be constitutional for a law to stipulate that someone can be forced to pay the bills of a random stranger?
I mean, the state already forces you to pay a portion of the bills of a whole lot of random strangers. That's what taxes are for. And sure, there are limits to taxation (and there should probably be limits to filial responsibility laws as well, like they can't force you to go brankrupt), but the principle that the state has a say in what people do with their money is widely accepted by all except the wildest libertarians.