We didn't have a VCR in our house until around '83, so I was 8 at the time. And back then, you really couldn't buy any movies so your timeline about videos being the babysitter is a bit off...
The reason I buy DVDs is because, as I said before, it's roughly the same price as renting. I can get DVDs for ~$7-8/each. If you rent, it's about $4-$5, and that's if you turn it in on time. This lets me buy the movie and watch it whenever I want without having to go Blockbuster to rent it. It's also cool to have friends over and watch a movie that you may have already seen but your buddies havn't so that you can get other people's opinions on the flick.
Also, a lot of movies are well worth multiple viewings to get some of the subtleties, sort of like how a lot of people here have watched every episode of Lost multiple times. You get more from the movie the second and third time. Have you ever re-read a book and gotten more from it the second time? Same thing.
The last reason I buy is because there are a LOT of extra features on DVDs that you just wouldn't have time to watch if you rented. Some movies have 2 or 3 commentary tracks, so that two hour movie takes 6-8 hours to watch if you want to hear the commentary. Who has time to do that with a 3 day rental?
I'm sure it's different for everybody, but those are the three main reasons that I prefer buying movies rather than just renting them.
CW