The exchanges such as Coinbase, Kraken, etc also lend and pay interest if you “stake” your coins.
Additionally there are what amounts to crypto banks like Blockfi, Celsius, Voyager, etc that do the same....lend your coins and pay you interest.
Like with a bank, you agree to allow the bank to convert your holdings and make you an unsecured creditor in the case there’s a run on the bank and they need liquidity. You agree to this as part of their terms of service.
In the US, the FDIC was brought in during the 30s after there had been several bank collapses. You can’t even run a bank if its not part of the FDIC which means for depositors, your deposits are insured up to $200K I believe? That is true even if the bank collapses.
International currency exchanges certainly do not operate like un-insured banks.
If they did, no one would do business with them.