I don't think this is useful.
Do Americans care twice as much about health as Swedes do, given that they spend twice the amount (% of GDP) on healthcare?
Does random-SV-billionaire care three thousand times as much as I do about time, given that he has spent $300k on an AP watch, and I've spent $100 on a swatch?
Also, someone that spends $300k on a watch isn't doing it because they care about time.
But, to your point about useful models, even if you do grant that on some level society does "care" more about something when it expends more money on it, can you tell from the outside view what it actually cares about? Most things that we spend money on are hopelessly complicated, and, like, some of the value we get out of, say, our expenditures on schools are "political favor for Democrats through the Teacher's Union" (and some of what we get from our expenditures on police are "political favor for Republicans through the Policeman's Union.") So do you get much useful information by saying, "Ah, we spend $X on thing A and $Y on thing B"? I mean, not much.
Uh, I'm pretty sure Swedes on average fight a lot less with doctors and pharmaceutical companies (and insurance companies) than Americans. The whole point of centralized healthcare is that it's both cheaper and less energy-draining for individuals because there's a small number of professional people paid to do the "fighting" (negotiating) on behalf of millions of other people.
But just like one USD in India is worth more than one USD in the US, it's not fruitful to naively compare the "amount of caring" by using GDP% as a proxy if the contexts are different enough. That doesn't invalidate the basic point of the article. The reason the US spends so much is that the US system is incredibly inefficient due to various coordination problems. If the US spent twice the money per capita and as a result had twice as good healthcare as Sweden then, certainly, you could say that the US cares much more about health than Sweden. But that's not the case.
And, like, it's always hard to get into the nitty gritty of why US healthcare costs so much, there's a lot of different things going on, but similarly you might say, "Okay, maybe the US has a 'coordination problem,'" but what does that cash out to? Hospital administration salaries? Again, are you gonna pick that fight? Providing extremely inefficient end-of-life care that still has at least some arguable benefit? Are you gonna pick that fight?