Navagon: I'd disagree with that. PS2 was designed with a small, blurry low res CRT TV in mind. PS3 was designed around a (roughly) 32" LCD screen. A massive step up. Even with all the TV enhancements since then we haven't seen that kind of a leap.
Your point would hold water if there wasn't also such a huge jump in graphical fidelity between the PS1 and PS2.
The other problem is that PS2 games started taking into account widescreen HDTV support before the PS3 was a thing. Games as early as Soulcalibur 2 (2002) offered 480p progressive scan support, which will give you very similar results to a 480p image upscaled to 1080p on an HDTV. PS2 games were being designed for that kind of display hardware a good four years before the PS3 game out.
Navagon: The question is: would a PS3 title look as good as a PS2 title does on a crappy, small old CRT screen if that PS3 title was reduced to a point where it would run on a PS2?
Well, given that I was playing PS3 games on a CRT TV through a SCART cable for about six months, I can safely say that, yes, even so, the difference was astonishing.
And I have a couple of cross-gen PS2/PS3 games where I can draw comparisons between the two gens: Call of Duty 3, The Golden Compass and Tony Hawk's Project 8. The then-new technologies like real-time shadowing, specular lighting and HDR made a night-and-day difference. Not forgetting HD resolutions of course, if you were playing on an HDTV.
Of course, there were various software implementations of specular lighting and a vague approximation of HDR in some games on the PS2, but they never came close to the generation following it. I think 24: The Game really was the only game that came anywhere close to looking anything like a PS3 title.
The differences between PS3 and PS4 are somewhat more subtle. The physical-based rendering that is mainly defining the "look" of many current-gen titles is actually easily achievable on PS3 and 360 (last-gen Metal Gear Solid 5 uses it), it's just rather expensive on system resources.
Other than that, the main differences really between PS3 and PS4 are slightly higher framebuffer resolutions, slightly higher texture resolutions, a greater focus on 60fps, slightly higher draw distances, slightly more refined particle effects - the new consoles basically deliver the power to do stuff that the last gen could already do but which was rarely advisable due to resource constraints.
It's a telling thing that Quantic Dream's "Kara" tech demo used technology that was developed and demoed for a PS3 but hasn't actually been implemented in games until a gen later.