Simply put, if you were required to have an internet connection to play one-player at home on your own console, you would need a stable connection. Even people who use facebook/reddit/etc don't necessarily have constant access to in-home internet. Particularly, rural areas that still rely on dial-up service (that's really a thing) would have difficulty playing games on a console they had paid for. Besides that, not every household has internet just because they have consoles. Just a few years ago, living in my mom's house, we did not have internet access. Not because we couldn't, but because she wouldn't pay for it. I played console games contentedly, but if I'd needed to "check in" once a day to play Katamari, I would have been SOL.