The practical tradeoff for not using the actual currency blockchain is instant settling time and 0 cost for transactions. If every transaction was on the chain,

The practical tradeoff for not using the actual currency blockchain is instant settling time and 0 cost for transactions. If every transaction was on the chain, they may take hours or longer to settle (not unlike trading shares on a "real" stock exchange), and there'd be a fee for each one. As for why they don't keep them on an internal blockchain, there's really no advantage in doing this vs a proper setup with a database. The part that makes crypto work isn't necessarily the blockchain, it's the public record part. Blockchain and crypto go together because the blockchain acts as a public ledger between parties who don't (or don't need to) trust each other. On an exchange, there's no trust issues- you and the person you're trading with have both agreed to trust the exchange and their records. Edit: I'm not super up-to-date on the crypto world, but I'm reasonably sure that there are on-chain/decentralized exchanges. I also think that there's been a lot of development towards making pseudo-on-chain exchanges through projects like the Lightning network in regards to BTC.