The importance of 3,000 hits traces directly to Stan Musial, I think. There was SOME awareness of 3,000 hits as a career goal going back to about 1908. I have an old, old Reach guide which has an article about the only players to get 3,000 hits in organized ball. As I recall, they thought that somebody named something like Emil Frisk was the only player to do it, most of the hits coming in the old PCL and other west coast leagues, and I think the article overlooked Cap Anson. There was an awareness of career totals, but very disorganized information and disorganized thinking about them.
When Cobb got his 4,000th hit I think there was SOME awareness of it, in the sense of notes in the newspaper, that sort of thing. But I believe that when Paul Waner got his 3,000th hit in 1942, there was relatively little attention focused on it.
Musial was the first player after Waner to get 3,000, about 15 years later, and for some reason Musial's 3,000 became a huge deal, a huge news event. It just evolved gradually until there was an opening for it to become an event, and then it did.