I think growing up with live TV made a big difference too. All the big movies/shows that were cultural touchstones for generations would be playing on repeat on one channel or another, so millennials would be randomly exposed to them without extra money/effort put in.
Nowadays, I don’t know how people who have grown up in the streaming era are supposed to find these movies, short of following a watch list, seeking out the right streaming service, and probably dropping some cash.