Not quite that simple, that’s vulnerable to an Eve-Alice-Eve attack. If $1B in BTC moves around in short succession the TXs can be linked easily. You need a mixer that splits up the amount to be paid out, and even then it needs to be done piecemeal.
There are companies (Chainalysis) that track blockchains and ‘grade’ wallets according to who they’ve transacted with. If enough of a wallet’s funds are from a mixer it may be scored a grade lower than the exchange’s KYC rules allow to do business with.
