Using Coinbase as a mixer is perhaps the least reliable alternative to anonymising transactions. After a certain transaction, Coinbase will ask you to provide them with ID verification and answer what type of transactions you're sending and receiving if you wanted to keep your account.
To simplyfy it further,they'd want to control what you can do with your bitcoins.The moment they find out something is against their policies,they'd call the FBI and give out your details and take control of your bicoins by locking your wallets.
Coinbase is NOT a privacy friendly service and their attempts to be in full compliance could have your transaction data shared with authorities (based on terms you agree upon when signing up).
Exactly!
TL;DR: If regarded as one, Coinbase is perhaps the worst coin mixerout there.
Coinbase is the worst thing ever happened to bitcoin.