They'd know who sent each utxo but you're right, they'd pool them in their own wallets. It's highly risky to try to earn any interest on crypto holdings for customers. The fiat accounts would tend to be compartmentalized, but maybe they can earn some paltry interest.

Custodians tend to charge for withdrawal or just bundle it all into their transaction fees. It'd be more accurate to charge for storage directly but it seems the market doesn't support this idea.