Two factors combined to kill BC: first, Sony removed it because having used a complicated architecture on PS2, emulating it completely required a dedicated chip on PS3, increasing costs (SW emulation working on a wide set, but not all titles, came quite later), then it realised that selling again revamped old titles not only made it save money, but even earn some more. The same happened with PS4 and PS3 BC, and this time probably both factors, costs saving and potential additional earnings were even bigger, as emulating the Cell would have probably required more HW resources even not doing HW BC with a true Cell chip, while very strong PS4 HW sales since the beginning, when its native SW library still have to grow, surely means an even richer market for PS4 editions of old PS3 SW.

Stwike him, Centuwion. Stwike him vewy wuffly! (Pontius Pilate, "Life of Brian")
A fart without stink is like a sky without stars.
TGS, Third Grade Shooter: brand new genre invented by Kevin Butler exclusively for Natal WiiToo Kinect. PEW! PEW-PEW-PEW!