I mean this as a genuine question (not an indictment), and as a complete blockchain/crypto noob who has just been a spectator:

Why is this the case? Isn't this like one of the best use cases of the blockchain in crypto? Why would they not utilize the technology to prevent this exact thing from happening? Are there tradeoffs I'm not aware of?

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.