Once the custodian is allowed to do anything that causes the exact tokens a customer deposited to be exchanged for another asset, that opens the door to FTX-style malfeasance.
If the exchange wants to offer interest-bearing deposits (eg: loan out your crypto), well then you'd expect to no longer be able to verify your deposits because you'd know they were loaned out, or that the exchange was trading with them, or whatever else. You'd also be forced to confront the fact that your assets are at risk at that point.
Right, but if an exchange took out a bank loan, the loan was recalled, and the exchange repaid it with customers' deposited cash and later goes bankrupt - possession is nine-tenths of the law.
Especially if the exchange intentionally has a structure that can avoid international tax laws - who's to say it won't also avoid international bankruptcy laws?
Then in this scheme depositors would be able to see that straight away, and force bankruptcy and asset recovery on the exchange while those assets still existed. This would (presumably!) stop the exchange repaying debts with customer deposits, because those customers would know straight away and could seek legal recourse against the bank and the exchange.
If you trust the fiat bank account statements, certainly.
Seems to me the problem of solvency at the boundary between the worlds of fiat and cryptocurrency is always present, and shuffling it around doesn't make it disappear.