Apart from that, in my country (not in the US, which is strange but it has happened) I have read that people with Coinbase accounts have been receiving this year a letter from the Revenue Services warning them about the fact they own cryptocurrencies, so they've had to declare them.
If you plan to fill your tax forms it is ok for you, but if you are not sure how to do it because in your country the laws are not clear, or you have very little money in cryptos and you didn't plan to declare for now, be careful with Coinbase.
Not just coinbase, any custodial wallet service that requires one to verify their account by fulfilling KYC/AML policy obligations should be avoided like blockchain wallet because once authorities or tax bodies go knocking on their doors, they will provide all the customer information required right from the time they registered on the platform.
It's also worth noting that coinbase has a mobile wallet where they claim that one has control of their private keys but It can still be linked to one's main coinbase account thereby compromising one's privacy.