Even though it makes sense for backwards compatibility to exist for the next consoles, I'll try to not get too hyped on that regard in case there is no B/C. However, shelving a feature like this would be idiotic since you want for your old library to be playable on the newer system.
But if this were to be true, I would really love not only for my PS4 games to be fully backwards compatible, but for PS3 games to also be playable through streaming.