Daytraders do not have too much of a choice, when they have a window of a few seconds to make their trades then they cannot hope to make their trade in time if they have to open their wallet, write the amount they want to send, sign the transaction, wait for a confirmation and finally wait for the exchange to acknowledge their deposit to finally be able to make their trade, by the time all of that happened the market has moved so much that most likely the trading opportunity has evaporated already.
This is the true answer. If they are trading, and they have a small chance to achieve what they are trying to achieve, spending extra amount and time to send the money from the wallet to the exchange and then trade, and trade back and send it back again all would be too inefficient.
I do not believe that we should be putting our trading money into anywhere else, if you are a trader then just keep it in the exchange. Hell, I do not trade that much and yet I still keep all my money in Binance, I just trust them more than I trust any wallet, and it is free to use them as a wallet as well, not only it is free, you could even stake or earn interest there as well.