You don't have the private keys. If coinbase loses them, you're out of money. Possibly. They're insured supposedly, but if you have your own private keys then the only entity you have to deal with in this case is yourself (this can be both a positive and a negative, depending on how careful you are)
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.
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.