Even if Sony wanted to, there is no point. CELL development had come to a hiatus state, since IBM is more focused on Power and PowerPC. If IBM does not develop new chip for CELL, there is no point to use it on PS4.I'm not going to criticize the decision not to include backwards compatibility on the PS4 given their choice of architecture moving to x86_64 (can't say I approve of the choice to go to x86, though; not a fan of the architecture). Hell, even if they stuck with PPC, backwards compatibility probably wouldn't have been worth it because of the convoluted cell processor they decided to go with on the PS3, and it would be a mistake to reproduce the cell structure with the new hardware.
But Nintendo has indeed shown a long history of backwards compatibility. You wouldn't expect the N64 to have it with the huge leap into 3D that generation, and you wouldn't expect the Gamecube to have it with the adoption of optical media.
When Sony designed PS4 they basically narrowed down to ARM, MIPS, and x86_64. Sony and Microsoft specifically picked x86_64 because it is developer friendly. It is an architecture that many game developers familiar of.