Immigration permission to work legally and tax compliance for the earnings are two completely different topics in probably all countries.

Even mostly law-abiding citizens with full work permission often dodge taxes in certain sectors of the economy - a common US example is restaurant workers underreporting cash tips on their tax returns. Plus, in addition to digital nomads, many freelancers (certainly not all) play as fast and loose with the tax rules even in their home countries as they think they can get away with. And much cross-border employment is disguised as independent contracting in ways that dodge employers’ tax burdens even when the employee has full work permission.

Conversely, there are already cases where even income earned illegally by visiting foreigners can legally be exempt from a country’s taxes. Example: Income earned in Canada by a US resident can qualify for Canada-US tax treaty’s exemption from Canadian taxation if the criteria listed in the treaty are met, regardless of whether the work was legal for immigration purposes. (Canada is actually one of the few countries from which foreign tourists can often legally work remotely for employers or clients abroad, but that depends on a lot of factors, and it can also be illegal like in most countries.)