Sure, but it took a lot longer and required a great deal more effort--though significantly less so once CDs came on the scene. Also, if just about everyone I knew at the time is any indication, we also bought quite a few albums.
I don't disagree with your basic point but Napster did change the equation. (I also tend to agree about what will happen if free streaming goes away--although the other dynamic in play is the many people who now expect instant access to a huge music catalog rather than owning MP3s. For them, having to go back to assembling a music catalog would be a big step backward even if they could do so for "free.")
What?? Before Napster, we made tapes. I still have tons of them. We exchanged tapes and copied them, and also we recorded the radio.
It was exactly like Napster, only much slower and complicated -- and also, in a way, nicer, because putting a tape together was a form of expression.
I don't think free streaming can go away without being immediately replaced by increased piracy, but we'll see.