And there it is. The old „privacy is not anonymity argument“. This tells me you either are a spook or been duped by one.
Without anonymity you don’t have privacy. Simple as that.
But to make it very clear:
You buy Sats KYC light, the exchange knows who you are and your bitcoin address.
You buy Sats on hodlhodl, counterparty knows who you are and your bitcoin address with very little effort (unless you go to extreme efforts).
Where the f is the privacy benefit?
You can only choose who you expose your info to.
Privacy after purchase is much more effective imo.