In general you won’t qualify for a work permit/permanent residency in most countries. And in general nomads travel on tourist visas (or visa waiver/visa on arrival), and those visas almost never allow you to do any kind of work, even online for a foreign employer. It varies by country. Some countries (and more ever year) offer so-called digital nomad visas, which are actually aimed at entrepreneurs, remote workers, and people who earn passive income in some other country. Those may or may not have local tax obligations, you have to look at every case.
Unless you go around telling everyone you are working remotely there’s little enforcement or attempt to round up nomads pounding on laptops in coffee shops, so digital nomads just fly under the radar working remotely and breaking the local immigration and labor laws. You can’t pay local taxes if you aren’t allowed to work and earn an income in the country in the first place.