> Is the middleman's nationality that important

No, it's not. You're absolutely right on that.

It's just someone you don't know who actually runs it due to no proper imprint promoting their business over someone else who you also don't know who actually runs it. So you send all your valuable business data to unknown guy A instead of unknown guy B. Oh, and also, in both cases you couldn't even sign a proper data subprocessing agreement with both guys. You can't sign it with guy A, who doesn't care, and you also can't sign it with guy B who says he's from Europe, does not even bother to provide an address to prove that, and obviously does not understand the GDPR.

Net souvereignty gain is zero by switching the middle man. In fact I'd say using such a "European" router service is actually worse than making business directly with, let's say, AWS, OpenAI or Anthropic where you'd at least know where you're buying from.