Streaming live games is not an option for me or over half of the US population.
I personally keep all my old systems. They aren't all hooked up at the same time. If I want to play an old game I can easily hook up the system and play. I always have several systems hooked up at any give time. I rotate them in and out depending on what I feel like playing. My Dreamcast has never been away from my TV since it's launch, which really says something about Sega's last system.
Since PS4 won't have backwards compatibility nobody should get rid of their PS3s, especially if they have PSN purchased games. I mean everything people have gotten on PS+ won't move over to PS4 so all that money spent on the subscription will be for nothing if you dump your PS3 for a PS4.
For me games are like movies and books and music. I watch Star Wars almost every year and I replay Mario, Zelda, and Halo from time to time. Old games are just as good today as they were when they came out and just like movies I know I'll want to enjoy them again.
I wish consoles always had full backwards compatibility with all previous consoles. It would makes playing old games much easier. Even with proper maintenance I know one day I won't be able to fix my NES or Genesis. That's why I keep a folder on my computer with emulators. One day the only way to play the console games I own will be on my PC and I don't believe there is anything ethically or morally wrong with playing a ROM of a game you own.