Why not use both? If your government requires KYC, you ain't getting around that. They want to track crypto the same way they track other assets, and that will involve monitoring all the on/off ramps. But once you have crypto assets, you now have the freedom to transfer them wherever you want, including wallets and exchanges that are more open/have fewer documentation requirements.

However, this freedom still doesn't exempt you from legal requirements, no matter how much bullshit you think they are. If the non-KYC exchange you transfer to happens to be under some sort of sanction, then you might get screwed if the authorities find out. Are they paying attention to you? Probably not. But it's up to you to decide whether the potential penalty is worth the risk.