I skipped the PS3 (my parents couldn't afford it) and for the longest time I wanted to play games like FFXIII, GoW 3, RDR, GTA V, TLOU, Killzone 2, Infamous, Demon's/Dark Souls etc... Years later, fortunately, I was gifted a PS4 with GTA V and TLoU Remastered bundled in.
I started the PS4 Gen by playing games originally made for the PS3, and I had no problems with it. I had a great time with those 2 games. Later, PS+ added GoW 3 and I played that too. But I was also playing current gen (by then) games, and I was impressed. Infamous SS, FFXV, RDR2, DS3, TLoU2, and others...
I was having the most fun while playing video games of my life. I had not played other PS3 games I wanted to play before, and I was fine.
Now most popular games of that era have been remastered for current gen systems and/or are available in PC (which most even non gamer PCs now should be able to run those games just fine). But I don't feel like going back anymore. It's great that they are there for if I ever want to try them, but I'm not holding my breath.
Perhaps most people feel the same way. They want to keep experiencing what's now and what's next. Maybe they want to experience specific games that were before, but most of those have been remastered or remade; many of which include better visuals and QoL improvements.
If that is indeed the case, then it doesn't really make business sense to invest resources for something that not many people will use, and if they do use it, it will be for very few and specific games. They will most likely make way more money with just remasters and remakes.
It sucks for people who have a PS3 library that they want to go back to but they can't. But if most Playstation owners that exist now never had a PS3 and a PS3 library to begin with, I can't see Sony finding any value in implementing PS3 BC. If they ever do it, it will be for desperate PR reasons (which at the moment they don't have) or the costs become insignificant for them. I don't foresee either happening any time soon.
I just hope this doesn't happen again for PS4/PS5 games. I will keep my PS5 as long as possible just in case.
TL;DR: Never.