If you want to keep trading with all of the money you put into the exchange then you might be able to hold it as fiat so it'll be better insured or withdraw it as fiat (if that's free).
Do you know anything about what strategy you might implement? For longer term trades you are more likely going to be able to afford to move the coins off the exchange, for day trades and similar fast moving trades you're probably better off leaving your funds on the exchange or splitting them between a few if you're that worried about one and have a good enough strategy it won't be too hard to recover your funds if one exchange is hacked (just make sure you trust all the exchanges you store funds on).
Yes i agre with you that thinks exchanger can cutting the fees.
If you do not have much money, it is best to keep it somewhere your fees will increase a lot if you do more transactions in which case you will lose a lot if you small trader. I hope the best thing is trade on the running and if you feel risk so withdraw every week.