Why do PKI schemes need security proofs? When it comes to designing new PKI-based key-exchange protocols, why are security proofs needed?

Without them, can we show a protocol's security? Does there exist a PKI-based key-exchange protocol that is secure without a security proof?
If you cannot provide even a basic proof of security, or a reduction of the protocol security to the underlying algorithms in use, you should assume the protocol is insecure.

Even with a security proof, a logical analysis of attacks against the protocol should be performed, as a proof may be limited to security against a limited amount of attacks, and in practice all attacks must be considered, even those that are uncommon or even impractical.