I wouldn't say the US being rich is a question of government organization, rather of not having been a colony whose sole purpose was to export raw materials.
Higher dimensions also means more tax collection, which could be perfectly invested into making the standard of living of Americans better (it seems absurd to me that you don't have any public universal healthcare). The government prefers to invest 50% of it in Defense though. Consequence (also) of arms industry lobbyists and geopolitical strategy etc. but certainly not of size.
Holding defense spending against the U.S. while comparing it to Europe doesn't make much sense. The U.S. subsidizes defense for Europe. Look, Europe spent the last several hundred years warring with each other, then stopped suddenly with U.S. ascendency. They didn't evolve beyond war. It just became unimaginable when the U.S. has all the guns and will enforce the status quo.
The European Union is widely regarded to be the main reason driving a peaceful Europe. I've not really heard of the argument at all, ever, that the US is what keeps Europe from engaging in war.
It's true that the US-led United Nations and principles of the right of self-determination led to massive post-war decolonization, leading to Europe being much less imperialistic (which accelerated the inevitable independence movements which were already in full force in most countries) but even here the US subsidizing defense doesn't apply, the amount of military power that was used for the colonies was quite slim, almost everywhere they became police-heavy, and the US wouldn't have subsidized colonial powers, on the contrary.
As for Europe warring until US ascendancy... while it's certainly true that the US was never more powerful relatively to everyone else than after the second world war, but they've been the largest economy in the world since the 19th century. They were the superpower before the first world war even started, let alone the second. Hell if anything, since then the US only lost power as Russia became a superpower, Western Europe became united and China rose, none of which were true at the end of the 19th century, and the per-capita wealth gap between the US and everyone else only slimmed since then.
But I'll agree with you on the fact that the US subsidizes defense spending through the NATO in the tug of war for eastern Europe, sure. It's unlikely that the EU could have grown eastward so much, without NATO we would've seen today's Ukraine happen much sooner with say Estonia, Latvia, Romania or Poland 10 years ago.
It's less a question of American economic power and more a question of the tens of thousands of American troops stationed throughout Europe. The U.S. military presence already in Europe is larger than the militaries of many European countries, and there's almost a million more American troops who can be deployed there if need be. If the U.S. was willing to do that in 1918, instead of turning isolationist again, World War II could have been prevented, just as the Pax Americana after World War II successfully prevented World War III.
The US has extensive public healthcare. Medicare and Medicaid are huge programs. I realize there is a fair chance that you mean some baseline universal care, but imprecise terms make the conversation more difficult.
Large corporations are also hilariously micro-socialist in the way health care is provided to workers (partly by government rule, partly because they hire productive workers and can afford to compete with benefits).
Edit: The ACA (Obamacare) was also a big step towards universal care. The funding/payment model is messy, but all someone needs to do in the US to get health coverage now is apply for it and make payments, they don't have to hope they get accepted by the insurance company (and I guess it is also much harder to drop coverage).
My notion of "public healthcare" is being able to walk into a government clinic or hospital and get free treatment or appointments as long as you show you're a citizen -- sorry for not having cleared that up.
I personally do like the single-payer approach, where you get coverage on a no-fee basis purely by showing you're a citizen/resident; and that's how it's done here in Denmark. But it's not the only way of providing universal care, even in Europe. Germany, Switzerland, and the Netherlands are typically considered to also have universal healthcare, but it's administered via health insurance, not as a single-payer model with direct state provision of services. There are various options for coverage, but having some baseline coverage is mandatory and intended to be universal (with subsidies for people who can't afford it), somewhat closer to the ACA model than to the Scandinavian or Canadian model.
I changed my original comment to "public universal healthcare". I once again apologize for the lack of clarity of the original comment, and I hope you understand what my point was.
Europeans visiting the states are genuinely worried that they will be carjacked, which I always find hilarious. Life is not like the movies or the news.
Higher dimensions also means more tax collection, which could be perfectly invested into making the standard of living of Americans better (it seems absurd to me that you don't have any public universal healthcare). The government prefers to invest 50% of it in Defense though. Consequence (also) of arms industry lobbyists and geopolitical strategy etc. but certainly not of size.