One of the reasons people prefer exchanges to Non- custodial wallets is because of the availability of coins to be stored on the exchanges than those wallets. Don't confuse cryptocurency (altcoins) and Bitcoin together, the suggestion of wallet you gave can only hold Bitcoin but the OP is talking about cryptocurency which is a terms normally used when someone wants to purchase other cryptocurency that aren't Bitcoin (altcoins). For this purpose exchange aren't still the best option because we have wallets that can hold more than two different coins on different blockchain as well.
We have Metamask wallet and it can be used to hold coins on Ethereum blockchain, Polygon, Binance blockchain, etc. You don't have to subject your coins to the mercy of centralized exchange to give you permission to withdrawal when you have a non custodial wallet like Metamask that gives you access to your private key and can be access on your laptop or mobile device. We also have some hardware wallets that provided this same service of having multiple coins stored offline out of the reach of hackers provided you keep your private keys off reach (online).