If you are afraid of the cost of ethereum gas, it is better if you store ethereum on an exchange so that you are not exposed to gas fees, it is better because ethereum gas is still unstable and it is true that gas costs always fluctuate every time this really causes problems for the current ethereum blockchain users.
It is risky to store your balance on an exchange. Even though you are avoiding the cost of ethereum gas, you cannot avoid the risk of losing all your ethereum if you store it on an exchange. I think it is better to pay transaction fees or the gas instead of risking all your money.