Imagine there were 2 editions of the PS4 - regular one ($425), and Enhanced ($525). The Enhanced version has a dedicated Cell chip from the PS3, everything else like the BluRay drive, memory, input etc is easily shared so the $100 extra is more than enough to make it happen.
Would you buy that?
$100 bucks extra for BC?
Absolutely! I want backwards compatability more than any other "feature" in the next system (take your "social features" and shove them!). I paid for the launch PS3 because of the backwards compatibility. It let me play my old games until something worth playing came out for the PS3 (which was a while...). Without backwards compatability, I will not bother purchasing the system until much later in it's life (when it's cheap and actually has all the features that they are "promising") if at all.
I would like Sony to make 2 models of the PS3, one normal "cheap" one for all the "unwashed plebs", and one that has all of the features that current technology allows. Hell, I would pay an extra $200. I payed $700 for the PS3, so why not?
I'm not going to spend an extra $100 for a system(s) I technically already have. That's money that can go towards 2 PS4 games. I'm also not going to sell my older systems just to pay for a PS4 with backwards compatibility. How many of us here have sold or traded a PSone, PS2, NES, SNES, N64, Genesis, Dreamcast, etc. and later regretted it? I'm not giving up my PS2 or PS3. Wish I could say the same about my PSone that died many years ago.