I've been playing a lot of PS3 lately, specifically making my way through the Ratchet & Clank series but not just that, and I think the games hold up extremely well. I don't mind playing games in 720p and while modern games have more refined controls and other conveniences (like better checkpointing) they really don't feel that different from 7th gen games. I compare something like Ratchet & Clank Future: Tools of Destruction to modern releases and while the game looks a little soft in places and has camera troubles it holds up pretty well overall. Then you think about games that were released 13 years before R&CF:ToD and you're looking at the SNES. It was the same amount of time between Donkey Kong Country and Tools of Destruction as between Tools of Destruction and today. The pace of game innovation has really slowed down.
On the other hand, while the games still feel relatively modern, using the PS3 interface feels like traveling back to another, much clunkier, time. Set aside the controller, which is bad but was really designed in 1999 not 2006, the ribbon menu system is not nearly as snappy or refined as it is on the PS4. It lacks some basic conveniences we take for granted these days like the ability to suspend games temporarily (sorely missed) and to take screenshots (it would be nice.) If you want to sync your trophies to your online profile it's a lengthy process that generally crashes the trophy system if you have a lot of games. Nothing feels reliable and everything lags.
Even worse is trying to manage your digital games, which can be kind of a nightmare. I wanted to download Ratchet: Deadlocked HD from the PSN store (don't judge me, you've done worse) and it was almost impossible to find it. The game is still for sale but apparently I got a free copy when I bought Full Frontal Assault. This meant that I could look the game up on the store but I could not purchase or download it, and because I got it free I didn't have an email receipt telling me when I got it. I ended up having to scroll through my massive download list on the store to find it, which took like 20 minutes because the download list itself is sluggish and unstable. Everything about that process is a pain and there have been times in the past when the store crashed a lot or booted you off PSN (thankfully it seems more stable these days.)
People are still playing these games. The Truetrophies.com site tracks when members win various trophies, and even on something as obscure as the HD re-release of Ratchet: Deadlocked, people have won the first trophy in the game most days this month. That's just among that site's relatively small userbase (about 75,000 people) so there are probably multiple people downloading that game every day from PSN. It shouldn't be that much of a pain.
Something people don't talk about when they talk about backwards compatibility is not just the ability to play old games that you already bought and are still fun, which is great and important, but also the ability to play them on newer hardware with all the bells and whistles. Xbox 360 games often look and run better on the Xbox One X than they do on original hardware, but even if they don't they're much easier to manage (if they're digital copies). The built in cloud saving functions work better and preserve your saves and make them portable better. The Xbox One controller is better than the 360 pad, so you get that as well (you can use a Dual Shock 4 with the PS3 but there are compatibility issues.) Console interfaces have come a longer way than game design in many ways, including built in streaming and much better digital management, and it would be nice to be able to take advantage of that.
One of the nice things that GoG does when it makes older games work on modern PCs is remove a lot of the pain that went along with getting old games to run on PC. You don't need to worry about IRQ ports or Soundblaster drivers, the games mostly just work, and within a much better environment than those clunky old OSs. For pre-seventh gen consoles that didn't matter very much because they had extremely limited operating systems and you almost always just booted to the game disc unless you needed to manage your memory card. But the PS3 era changed that, with digital game libraries and installations of even disc-based games, and those old archaic systems are a pain to use now. Hopefully the PS5 will be an equal leap over the PS4 in terms of operating system functionality with more reliable suspend features and even better streaming/sharing functions. It would be great to be able to take advantage of those features on older games. And that's before we even talk about how nice it would be to be able to pack up my PS3 and not give real estate to it. The games are still good. It's the system that feels old.