Coinbase isn't the best choice because you don't have a access over your private keys. That's why like many users I prefer non-custodial solutions such as Coinomi, Atomic, Ownr wallet and etc.
Wrong, your reply would have been correct back then when it was Just the
Coinbase web interface and app (a simplified exchange and custodial wallet) and
Coinbase Pro, formally GDAX.com (Coinbase's advanced exchange).
I guess due to competition the brought a new product to the market, A wallet that's noncustodial and lets you have control of your seed phrases and private keys but it's only mobile based as of today.
https://wallet.coinbase.com