Op, not your wallet, not your coins is not a recent statement and it has been on ground for years. Nobody that is well knowledgeable in bitcoin will not advise you to save bitcoin in centralized exchanges though you can use it to buy bitcoin and once you bought it you have to send it transfer them to self custodial wallet for safety purpose.
In the centralized exchange, it is not only hacking that can make one to lost bitcoin but all things which we have discussed before. And such are, account frozen, Blocking and restriction. If you account is suspicious, they will block it and ask you to do verification and if the verification is not accepted then your account is permanently blocked.