Applying for a visa with work entitlements is a completely different scenario from doing remote work on a temporary entrance visa. Which is what most digital nomads will be using (without creating any foreign tax liabilities for themselves).

Even then you’re confusing tax residency with tax liability. You can arrive in a country, and immediately create tax liability for yourself (by getting locally sourced income for example). But you’re not going to get tax residency until you’ve spent some minimum period there (usually ~6 months), even if that residency is back dated to the day your first arrived.