Earlier quoted context omitted.
While an EU citizen can at least roam in the EU fine, and a US citizen can roam the 50 states, seems that roaming outside of that would be exceedingly difficult and expensive to get appropiate visa (if they exist)
What makes you say that? Admittedly most of my backpacking-like travel days are long behind me, but border crossings typically aren't that difficult or expensive. EU is probably the hardest (almost certainly needed the visas before you arrived). Most of SE Asia and Africa you'd just hand over a few USD at the border, get a stamp, and keep moving.
I as a UK citizen can temporarily visit the US, or Japan, or Thailand on holiday.
I could also go to meet my colleagues there, go and sell something, go and buy something, go to a convention, etc. That's counted as "doing business"
I can't work there though, unless I have an appropriate visa. Doesn't matter if I'm working remotely for a remote company that doesn't even have a presence in the country, it is still doing work.