Backwards compatibility is important to me, and I do use it quite a bit. I wish the PS5 was fully BC for a couple reasons:
1. I originally had a fat 60GB PS3. It was glorious. I could play PS1, PS2, and PS3 games, all through HDMI. Unfortunately, it started displaying graphical glitches after a while. So I had to replace it with a PS3 that no longer has BC with the PS2. W had also previously sold the PS2 since we no longer needed it. I would happily go with a 60GB PS3 and PS5 as my all encompassing solution, but buying one of those used today is really just gambling that it will last.
2. Even if I did have a PS2, the best that thing can output is component. Aside from the fact that component is considerably lower quality than HDMI, most TVs today don't even have component ports anymore. It is increasingly difficult to actually play a PS2 today.
Right now, I resort to emulation on my PC for my PS2 needs, which is pretty good, but not perfect. Would be nice if Sony provided a method.
Component is not lower quality than hdmi with decent equipment. Composite video is the lower quality one. My ps2 with component cable looks just as good as ps3 through hdmi, same with the 360 in 1080p over component cable, zero difference with the later HDMI revision.
If your tv doesn't have component video input you can use this
You can of course still use the digital sound output from the ps2 direct to amp for better sound quality. There are converters with digital audio as well but they are a lot more expensive
It's very easy to play a ps2 nowadays, there's actually an all in one solution so you don't even need the component output cable for the ps2 or extra power cable
Yes, component is good, and certainly better than composite. But no, it's not as good as HDMI, at least specifically in terms of PS2 vs PS3. I had the PS2 component cable back in the day. It only outputs at 480p. It was an obvious improvement when I got the PS3 and started playing my PS2 games there, even if it was only upscaled. It's a cleaner image. And that's even before talking about the convenience of having audio and video in one, being able to play all your games on one system, not having to buy converters, extra cables, etc.
My PC is hooked up to the same TV as my consoles, so unless Sony throws us a bone for BC, I'll probably stick to emulation (of my legally purchased PS2 games, of course).