Ok, so I think now I get your point.

The term "unhosted wallet" was used by governments when we already had a term for that ... "wallet". That's it, it's a wallet, not an "unhosted wallet". But governments wanted to make "unhosted" be an attribute that helps with their argument that unhosted wallets are the outliers, and the ones for which regulation is needed.

And that's total nonsense.

So now (I think) I get your point about KYC-Free.

Bitcoin that has no tie to your identity is not "KYC-Free" bitcoin, ... it's just bitcoin.

And that If you have bitcoin that is tied to your identity, then that can be called "KYC" bitcoin -- because that is bitcoin with some other attribute (specifcially, a tie to your identity).

Am I getting closer?