[smeej]

There is a "Coinbase Wallet," though, which is somewhat confusingly a separate app where you actually do hold your own private keys.[0]

You can seamlessly link your exchange account and your Wallet account so you can move the money right into your own Coinbase Wallet with your own private keys as soon as you're done with the exchange.

I'm not sure the parent comment meant that wallet, but Coinbase does "give you a wallet" if you want, complete with your own private keys.

[0] https://wallet.coinbase.com/faq/

[brianvli]

You need to transfer the funds from your Coinbase account to Coinbase wallet. You’ll never have access to the private keys on Coinbase.

At that point, Coinbase wallet is the equivalent of Metamask et al

[smeej]

It would be, except that you can easily link the two accounts. Sure, that's roughly equivalent to making sure you have the Coinbase exchange address assigned to your wallet loaded into Metamask and your Metamask address loaded into the Coinbase exchange, but that takes a level of understanding that linking Coinbase Wallet to Coinbase exchange doesn't require.

Coinbase does "provide you a wallet." It just isn't part of the exchange.