While funny, the whole idea of tracking your data enough to give you a wrapped kind of goes completely against everything these extensions are supposed to do.
My suggested alternative is you click the wrapped button and it just says:
“Fucked if I know! ¯\_(ツ)_/¯”
Absolutely, I don’t think having non anonymous areas of the internet is necessarily an issue, so long as we also (can) provide plenty of non anonymous areas as well.
Anonymity has its downsides, and transparency has its advantages too, not just for the establishment.
It’s just important to keep fighting for and protecting the anonymous bits in parallel.