That’s literally what caused bitcoin mixer services to exist where you throw some amount of BTC in an account with them, tell them how much you want paid to whom, and then it takes all the transactions for a certain (usually random) time period and plays a shell game with them, passing funds from account to account in various amounts and resulting ultimately in the right amount going from you to the target via multiple intermediaries. Slow because it involves a lot of transactions, but the idea was to make it hard to trace exactly who was paying who, beyond being able to know that one or more of the user accounts were paying some amount to one or more of the destination accounts.

Over the last 5 years or so, law enforcement has been shutting down several such organizations for money laundering, being illegal money transmitting businesses or things along those lines as appropriate to the jurisdiction.

Even without them, with good opsec it can be hard to tie a BTC wallet address to a human person, which is the point of anonymous payment.