Have you ever worked for a company in Country A and been sent on a business trip to Country B? Most likely your company didn't need a Country B working visa for you, just for a business trip.
I am not a lawyer, but I don't see how the digital nomad lifestyle is any different. If you're just spending short amounts of time in these countries, legally how is this any different from going on a business trip since your company and salary will be paid in the origin country.
I'm sure there's a cut off point, like once you go over a certain amount of time it becomes harder to justify your trip as a short term business trip... but what's that line?