This is mostly how things already work under EU rules. Neither the original "right to be forgotten" established by a significant court case, which in fact did r

This is mostly how things already work under EU rules. Neither the original "right to be forgotten" established by a significant court case, which in fact did relate to systems like search engines, nor the subsequent "right to erasure" under the GDPR creates an unrestricted power for data subjects to require all data about them to be deleted regardless of circumstances. For example, you can't take out a bank loan and then force the bank to erase all records of it. There is at least one significant deviation from your "transitive" reasoning, though, in that while EU law might not extend to an original source that is providing misleading/harmful data about someone but is based elsewhere, it can still affect those providing indirect access to that data who are within the scope of EU law.