> Basically every US company operating in the EU is breaking GDPR post-Privacy Shield right now: it's illegal to transfer data of EU residents to US data centers.

This is not true and the devil is in the details. It's illegal to transfer "personal data" of EU residents. The definition of personal data under the GDPR is what US companies would consider PII or personally identifiable information and not all companies collect PII. In fact, I would argue most companies go out of there way to not store PII.