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.
If holding ETH for a long time on an exchange is not recommended for any reason because without a private key, your address cannot be fully recognized, the risk of hacking an exchange or private exchange account is very possible. the best wallet security option is to store it in a personal wallet or cold wallet.