You can get BC by using hardware that's an advancement of the old. All them systems were departures from what came before and they chose to do the same with the PS4.
I feel the ps4 coulda got away with having a better cell CPU. Though I think I heard IBM left it or some other crap. The thing is that it can meaningfully help the GPU. So PS4 could have saved money on developing a CPU and just gone with a beefed up cell, put in a better GPU than they have now and then, on top of that, they can boost the graphics if needed with the new cell CPU. My naive thoughts anyway. I think a future where the CPU and GPU aren't so seperate would be beneficial. Like unified memory (which the ps3 lacked). Instead they dumped it and are doing away with all the knowledge devs have gotten by working with it. So now, if they want to make a ps4 game that would also be on the xbox360 and ps3, they have more work on their hands. If you think about it that way, they could really have come out on top. Dev a game for the ps4 and its as easy as anything to sell it on the ps3 etc. Easy to port ps3 games to ps4 with improved performance and graphics. Lots of possibilities but people cried and sony listened (if they had a choice).
PS3 will start getting neglected ASAP. Soon as Ps4 sales reach a good amount, putting a game on the ps3 would be too much of a hassle. We'll likely end up with games showing up on the 360 and next gen consoles alone.