Well, to the OP's question about what happens when the exchange freezes the wallet, well, if he is talking about the money in that wallet, then that becomes the custody of the exchange in case they never unfreeze the account and keep the money with themselves forever. That is another way of scamming people, and therefore, one should be selective and careful in depositing money in centralised places, including exchanges or any service providers.
Not for one day an exchange wallet is a personal custody, just because they allowed you to freely use the wallet without any prior warnings or quick note doesn't make it a good one.
I don't have problem when people used centralized exchanges but making an exchange as place of storage kills everything about Bitcoin or any coin you decide to keep on the exchange, there are plenty ways to have coins under your custody, way cheap and more secure than when you allowed everything on another third party custody.
There was a time Binance was locking funds due to geographical concern. I remembered one time when Isreal and Palestine where into one or two disagreement, I don't know what happened then but Binance began to froze Palestinian Binance for no reason and they had to even respond to the allegation to be truth. Like it's the confidence for me. If you have funds on any exchange, don't let it sleep over on the exchange, withdraw your coins before you sleep.