The funny thing about this is that Sony used to be the best option for BC on Consoles. They have a long history of doing it, and doing it well. The PS4 is literally the only time they have never offered it. They can do it, they just need to have the inclination to do it. But after this gen, it is hard to say if they do or not.
PS NOW has nothing to do with BC, and if anything, BC makes it more appealing. PS NOW is not a replacement for BC, but rather an investment for a coming streaming focused future. If it was just for BC, it wouldn't offer PS4 games, nor would it be available on PC. Also, think about it for a second: with PS3 BC, PS NOW would suddenly have a full downloadable library of nearly 800 games (probably more when PS5 releases), all of which are natively playable on your Console. That makes it one hell of a proposition. It undeniably makes the service itself more appealing.
Now, I understand that allowing BC means people can have access to their PS3 libraries for free, but does anyone really have over 600 PS3 games lying around? Probably not, and in that case, PS NOW still has plenty of value regardless of free access to the games (not to mention there are many people who never owned a Ps3, or sold off the system and their library of games after PS4 launched without BC). I don't think it hurts NOW at all. Honestly, having the entire library be downloadable would probably make me a subscriber.