If you are trading then you need the money at the exchange to trade, Centralized exchanges will need you to deposit the asset on their wallets in order to trade. Now the point is that as long as you dont hold the private keys to a wallet those coins are not yours. Truly speaking you are trusting the exchange with your money when using it and so after doing the exchange you should withdraw the assets to prevent theft in case of the exchange getting hacked or exit scammed.
Again you cannot trade from your own wallets directly on a CEX, maybe DEX are capable of allowing that but we are yet to see DEXs that run bitcoin If I am not wrong, most of them allow Ether<>ERC20token.
Of course while exchanging on a CEX your money needs to be on exchange and yes you are at risk of theft by the exchange at that time.