Where do daytraders store their crypto?

Assuming you trade a lot and are a daytrader and use binance, coinbase and all those exchanges, you need your coins on the exchange to trade. But when you are done with trading that day, do majority of traders just leave their coins there till the next day? Now if you are trading it with USD, then no issue then right since the balance would be USD or a portion of your balance is in USD?

If you are doing this with coins like ETH, you are going to pay a ton of fees each way. Your exchange is going to charge you a fee and you going to pay a decent fee sending it back the next day. Now imagine having many other altcoins where the fees are similar. I can’ t imagine people are depositing/withdrawing each day? The deposit/withdraw fees would eat them up if they do ETH or even if they use a lot of other coins because the exchange is going to charge them a flat fee each time.

Obviously keeping your coins in an exchange is not as safe as a hardware wallet, but what do daytraders do? If I daytrade, I would just keep my coins in the exchange until I need to withdraw or if I know I won’t be trading for a while. The other thing is some coins they want to trade, it is possible they can’t store it in their hardware wallet because that coin is not supported. So because of that, no other option than to store it on the exchange? Or they use something like metamask? But still they have to pay fees depositing/withdrawing right?