I think the rationale for ignoring per-capita is that you're talking about the wealth of a "single entity", the US. And, well, yeah... ok, I guess (ignoring the fact that, as you point out, GDP is more like income than money in the bank).

I agree that looking at it that way is meaningless for the purposes of figuring out whose populace is the financially healthiest, but... that's what people do, for some reason.