But when Youtube shares the key with me/my client the first time, is that also encrypted?
Here’s an explanation of what happens during the initial TLS handshake.
…if ISP automated the process of gathering keys and decrypting web traffic for a certain site with them for all users, would that work for them?
Not sure this is exactly what you’re asking, but there’s the concept of forward secrecy for defending recorded encrypted traffic from future key compromises.
Looks like someone cropped the attribution, but this was actually created by a friend of mine. He’s got some of his stuff available here: www.redbubble.com/people/comicalconcept/shop
EDIT: I think he made this stuff back around 2010. Wayback machine has his old site with higher res versions, including this one.