Jesus. This is not complicated. Just go to a country for as long as the tourist visa will let you (often 3 months or so), and work there, and enjoy it. Don't offer to pay tax to that country unless you want to. You only get one fucking life!
I'd probably hesitate to, say, rent a co-working space if I were technically required to have a business visa. But so long as I'm not speaking at events, meeting with customers, etc. absolutely no one cares if you're working on email, programming, writing, etc. on a valid tourist visa. (And, as a US citizen, aside from a few countries with somewhat onerous visa policies in general, I have absolutely never had an issue come up where I needed something different from whatever on arrival paperwork there was.)
I know right? And you got downvoted too. These people are so neurotic!
Haha I was going to say all us sane people should get in a taxi and go some place one day. But net positive 5 upvotes now. Sanity prevails!