It depends which exchanger you choose to trade. Like I kept some coins 900 USD worthy in Binance to trade, still, I haven't withdrawn them, they are safe in Binance exchange, the same thing I did in bancor exchange. So. if you trade in well-reputed exchanges which have strong security options then I think you can keep your tokens there. No need to spend some extra fees.
Keeping coins in an exchange overnight is something that should not even be a thing as long as what you have on the exchange is your trading fund, why will you want to be moving it around.
Just make sure your funds are secured by at least making sure you are using the additional securities present on the exchange like 2FA to secure your account from getting hacked, but most especially, always make sure you are on an exchange with something you can afford to lose, because anything can happen and since it is a centralized exchange, you really may lose everything if something terrible happens.