Are you talking about a potential situation where a Drugs-R-Us are using (for example) an American service, but directing them to store it on EU servers?

Or are you talking about Drugs-R-Us using a non-American service in general?

The internet however is not limited to US and EU. Criminals have always been using services all over the globe.

Ah, Americans. "Valid warrants and court orders" are national. Unless there are international agreements (of which there are many), whatever Bumf** PD, Oregon does should have no impact on what a Lithuanian server hosting company does. Of course, this is not how it works in real life and many non-Americans consider that abusive, and rightfully so.

FYI - this kind of extra-territoriality was what started WW1. An ethnic Serb Bosnian (Gavrilo Princip) shot the Austro-Hungarian heir apparent and as a result Austria-Hungary sent Serbia an ultimatum.

The ultimatum contained lots of harsh terms, which Serbia accepted, except for 1. The term they refused was to allow Austro-Hungarian police, prosecutors, judges to directly investigate, arrest, prosecute and imprison Gavrilo's possible collaborators. And the reason they refused that was because it's basically giving up sovereignty. Once you let another country send their police force investigate, arrest, prosecute and imprison whomever they want, they have full control. They can imprison your prime minister and you have no recourse except for starting a war.

So Serbia accepted that if it wanted to remain independent, it would have to accept fighting a war.

I have yet to see the EU ignore a valid judicial warrant except in the most extreme cases.

The point, however, is that you have to have a valid judicialwarrant and not some random-ass piece of paper generated by Adderall-addled sycophants of fascist South African nepobabies.

By many measures Europe is in fact pretending to be sovereign. I think it is what they are attempting to do at the moment, "stop pretending to be sovereign" and actually BE sovereign. At least that seems to be the claimed attempt.

If anyone is not sure why I would say that Europe is not sovereign, I will answer that question if you ask, but considering the current state of things and even just this discussion about data sovereignty and other related topics about using and deploying European technologies; I suspect most, if not all have a sense that Europe is in fact not sovereign... and that's without even pointing out huge elephants in the room like the 275 US military installations across Europe, and not even to touch on the fact that NATO is really just ** pulls curtain back ** SURPRISE! ... America, Europe Division.