Once people get paid and pay in bitcoin, that anonymity is guaranteed.
The issue right now is the bridge btc / fiat, where people get doxed, if that bridge does not exist, bitcoin is anonymous, if you want to.
Discussion
Leaking unnecessary data is detrimental to that anonymity. If I naively send/receive Bitcoin my counter party, and anyone looking at the blockchain, can see amounts and past/future interactions with other addresses. Every additional point of data is another piece that can potentially aid in unmasking you over time especially combined with other information offchain. Not even Monero is a silver bullet much less Bitcoin.
But agree that the fiat KYC bridges are the largest (but not only) problem