What you're saying makes sense. Any data derived from PII should considered as PII itself if it can be used to identify users, and even if it cannot be used for that, it needs to be cleared frequently enough such that you don't end up with data derived from information for which you received a deletion request, for instance.

In practice, you can achieve this by simply refreshing your derived data frequently (ever ~30-60 days), and for aggregated data k-anonymity is a good way to enforce this privacy constraint.

https://en.wikipedia.org/wiki/K-anonymity