Hi - I'm an American (although dual citizen with Canada) who worked in US government for six years (at the Fed and the CFPB) and am now an academic in the UK so happy to give my thoughts briefly; feel free to reach out if you'd like to discuss further.
I agree with the general premise, both because the US is so large and because (for better or worse, and despite everything) the US is still seen as a leader in many ways: whether or not they copy it (often not, often with good reason), almost everyone will at least consider doing anything the US does. The US system has more built-in checks & balances than the UK's parliamentarian system, which can limit scope for progress, but that's mostly at a high level (which is important, but not where most of us will have impact anyway). Similarly the federal system implies more decentralization in the US, which also limits the power of any one actor (federal or state or ...). However in terms of the bureaucracy there is a lot of scope for action in the US, e.g. one of the few complaints about the CFPB that was actually true was that it had a lot of power (again for better or worse, but it did and to a lesser extent still does).
In terms of research (and non-profits, which I know a bit but not as well), you're right that it doesn't matter as much -- except that the best research in many fields happens in the US, if only because it's a coordinating device and had increasing returns to scale (once the best start coming, they all want to be there). This is certainly true in my field of economics and behavioral science, and I suspect (happy to be corrected) true in many relevant technical fields (climate change, AI, animal cognition) although perhaps less true in something like philosophy.
As others have noted fit and opportunity are probably more important than any of this, but on the margin yes I think there are good reasons to be in the US. [Why did I leave? Partly because my wife is European, and partly just because the senior academic job market is very thin and this was an offer at a good school in a nice location.] And yes, unfortunately I suspect that the Selective Service tickbox may stupidly cause problems; they certainly checked mine when I joined in a standard role. I had somewhat randomly done it when I turned 18 many many years ago and then completely forgotten about.