Sony made a HUGE bet with PS Now, streaming is the future so it seems. Is probably true that bring back to life that backward compatibility could a pain in the arse, but there's no logical excuse other to force the consumer to get their services and forget and probably bury that nostalgic *what if..we can run PS3 games discs with a Next-gen console*.
There are some PS4 gamers and media members that think Sony should investigate rolling out a backward compatibility feature for the PS4 - just to make gamers happy. Sony has worked hard to create a good gaming ecosystem, trying to keep sometimes fickle fans happy.
If it doesn't offer backward compatibility, Sony runs the risk of leaving gamers disappointed, though with other methods to play PS3 titles - for free or paid rental - I think the Japanese electronics company has done enough already.
Sony initially seemed skeptical of Microsoft's announcement regarding the Xbox One's backward compatibility, doubting whether it's possible - and that it would involve "lots of engineering effort."
Regardless of what PlayStation gamers want, it seems unlikely that Sony will try to follow in Microsoft's footsteps anytime soon.