I would ask a simple question. While an SSL connection does initially use a key pair, the first thing it does is switch to an asynchronous cipher. Naturally, you could catch the cipher key at the beginning of the handshake, but if you don’t catch it you can’t read the traffic.
When you spend all those millions building special hardware you don’t miss the cypher key.
Not quite the right term, but right idea.
The key exchange is to establish a symmetric cipher like 3DES or AES.
https://en.m.wikipedia.org/wiki/Symmetric-key_algorithm