Currently exchanges with cheap ethereum fees are on the FTX market. you can register an account there and buy ethereum to get cheap fees, you can buy easily without KYC. however, it can only help there, if you transact with the MEW wallet then the gas will be the same high.
Sending the ETH out of the exchanges also charges high fee, the exchange fee might be cheap but the transaction between exhchanges or from the exchanges to wallet also requires high fees. So i think right now the best way to save ETH is just save it whereever the ETH locate right now and only send them whenever we want to cash it out or buy another coins