They could, but generally it is expected that before a subpoena is complied with it is checked to be compatible with the laws of the country it’s in, and requires cooperation from that country. Most often they are ignored if there’s not a presence/entity/assets in the US.

It’s also hard because no individual case would likely justify a move like that. It would have to be the sum of many, many cases.

Not every judge agrees with your statement of the law of privilege.