Most exchanges that require KYC are centralized, meaning they have to follow the government's rules and regulations in the countries where they operate. We used to have plenty of non-KYC exchanges, but I guess many couldn't handle the governmental pressure and started implementing KYC as a condition to use their services.
On the second point, with non-KYC exchanges, you actually have control over your own private keys. The exchange gives you your private key and a wallet to store your funds on their platform. So even if they shut down, you might still be able to access your money.
As for the third and fourth points, sure thing! Whether KYC is involved or not doesn't stop anyone from sending or receiving coins. But connecting your non-KYC exchange back to a centralized exchange kind of defeats the original purpose.