When I got the XSX recently, it was so I can play Starfield when it comes out. That was basically the only reason. I did not realize the extensive backwards compatibility that this thing has. But since getting it, I've been playing FF13 trilogy, Fable games, Dragon Age series, Lost Odyssey, etc. Basically all games of note going all the way back to the OG Xbox will play on the latest console. Either with the original disc, or you can even purchase them online.
The point of my post is I think it's a real travesty that PlayStation doesn't do this. I don't understand it. First of all, you cannot buy most PS1-PS3 games on the digital store. You can't use the discs. The main way to get access to these games is through the top tier of PS+. But the selection is quite limited, and PS3 games in particular are streaming only.
With the selection, I want to point out that you can't even play most of the Killzone series on PS+. This is a first party title. There is absolutely no reason that Killzone shouldn't be available. Killzone 1 isn't even on there. A PS2 title that is not graphically demanding.
As for the streaming of PS3 games, maybe this was justifiable back on the PS4 because the PS3 has a unique architecture that can be difficult to emulate without performance drops. But with the capabilities of the PS5, it's not credible to claim that it can't emulate a PS3. It certainly could, if Sony wanted to assign resources to make an emulator.
I am not a fanboy of one or the other, and I probably still play more on the PS5 than my Xbox, but I think Microsoft should market their backwards compatibility superiority a lot more than they currently do.
The simplest and most likely reason is just because they don't have to. Playstation is leading Xbox by a lot this generation (so far, things can change) and PlayStation just has no incentive to add value to something they're already selling record numbers of. Xbox is trying to attract customers, customer playstation has left on the cutting room floor, and backwards compatibility is a way to do that.
Not to mention the closer you get to modern day, the more games rely on company servers to remain running. Long gone are the days of simple platformers like Super Mario Bros. Many games made in the last 15 years are multi-player games with a basic ass single player added on for 'compliance' reasons. It'd still be great for those that want it, but I don't feel like I'm missing out on much that I can't replicate myself with ROMs and emulators should the need arise.