No, it shouldn't, and Kaz himself basically said so right before the PS3 launched. The PS4 should be HARDWARE BC with all former PS consoles as it's basically pennies on the dollar to make the PS1 and PS2 chips. The Cell would cost a tad more, but again, it's now 7 year old tech.
I'd pay $600.00 again for full BC and I know alot of hardcore gamers would as well.