Why not verify the KYC process? Do you hide something?
I'm using Binance but without KYC I couldn't use their other feature like P2P that's why I end up verify their KYC process. I feel safer on Binance than on other exchanges.
Well, I think they just want to avoid money laundering.
Anyway, another option for Binance as suggested above is P2P exchange like Bisq they don't require KYC verification.