On the OTC side (which I guess you’re referring to?, CB sets their own spread , which makes it more akin to a fee. Even if CB is technically correct saying “0 fee”, they can still charge any price they want for buying vs selling.
Owning the actual asset and not just an IOU
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.
At that point, Coinbase wallet is the equivalent of Metamask et al
Coinbase does "provide you a wallet." It just isn't part of the exchange.
Personally, I think unless coinbase pivots, their current business model is not sustainable in the long term. But right now, coinbase is capturing value in a way that the early majority of crypto's adoption curve can digest.