Why does anyone care about playing old games on their next gen console? This is coming from a guy who still plays his PS3. I just, you know, use my PS3 for that. It works just fine. I don't even think most people use the backwards compatibility function very much at all if it's in the console. Ultimately it's a waste of resource, not to mention it's probably impossible for Sony to do it considering the different architectures of the machines.
That being said, I will say that Sony has done an absolutely terrible job with PS Now. That could have been a good solution to backwards compatibility and more, but the pricing and them making you pay for games you already own is just ridiculous. At the very least these games should have been heavily discounted, but that's not possible since most games aren't available on the catalog, even popular ones from last gen.