They could handle the KYC aspect of Monero coming into Coinbase the same way they do for cash and bitcoin currently, and the same way banks do. I.e. ask the owner to disclose how they acquired them, source of funds, etc.
Banks have rules about cash. Coinbase does not handle cash, only bank transfers and Bitcoin (and Ethereum).
That's a big difference. A bank could just throw up their hands and say "Can't trace the chain? Let's treat it like cash to be safe" but Coinbase can't in practice do that.
In my quote, I guess instead of cash, I meant USD. If there is a large deposit of USD, they often ask for the source of the funds, employment, etc. to fulfill their KYC. Other than asking those questions, they have no way of verifying where those USD actually came from. They just don't accept them if it raises flags.
If they did accept cash, they would ask the same questions for large deposits. Same as if you deposit large amounts of Bitcoin or Ethereum.
Which is why I think its the anonymous outflow which is currently the bigger problem for them.