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.

OriginalSize

Most do, even if they don't make it transparent. At the least, I would assume a custodian might use the funds they are holding to earn interest. I'm sure that there are laws regulating this, but I am very doubtful wallet of satoshi or fortress just have piles of bitcoin sitting around with labels next to each utxo saying who it belongs to. 

Scoresby

bitcoin

Self-custody costs money

I've often thought custodians should charge. Exchanges don't want to do that because it removes liquidity. I guess SN wouldn't want to do that because it removes liquidity. Still there is risk and there is effort so a nominal fee makes sense.