But if you're going to use them as an exchange, there's no problem but AFAIK, you'll be required to comply and be approved through KYC.
The problem is the complete lack of privacy or security, your data being share and sold across numerous third parties, and your activities being tracker, monitored, and reported to your government. If you are happy with all of that, then you can use Coinbase to trade coins, but you should remove any and all coins from it as soon as your trades are complete.
Yeah, aside from the KYC, there goes those consequences that OP and the others who would like to do it with CB.
Just for the sake of trading, should he be aware of those things so that he won't be surprised if something unexpected happens to his information being sent to them.