Except you're only picking games that support your case, and you're ignoring the impact that graphics can have on atmosphere.
Would a game like Fatal Frame work nearly as well on the PSOne or Saturn? It would probably still work, but not nearly as well (Silent Hill is the exception here, but that's because the game is able to get away with never really showing anything in any sort of detail). The same goes for Doom 3, which bases its entire premise on the graphics. But they're not there just to make you go "wow," they're there because powerful imagery can have a huge impact on how someone perceives a game. Play Doom 3 with all of the effects off, and then again with all of them on. They
feel drastically different because the feelings the game creates are so central to someone's enjoyment of it. Remember Burning Rangers on the Saturn? Now there was a game that could have benefitted from better hardware.
Half-Life 2's physics would not have been possible of previous systems. Period. They're simply too complex and often work on too large a scale. This is one area where added processing power has had a positive impact, because certain games can definitely benefit from more realistic physics. AI has also made dramatic improvements over the years (remember the days when it was impresive if an enemy knew how to take cover?).
Also, I have to wonder why you used the progression from GT3 to GT4 as an example of why new technology isn't needed, because there's no real advancement there.
Both games are on the PS2. If anything, the lack of advancement would indicate that newer hardware is needed if we want to push to push the envelope further visually (though I'd argue Polyphony is just a lazy developer and have been rehashing the same game since part 2).
In addition, how is it any different at all from the arcade days? Arcade games were just like home games, except more powerful. It's the exact same scenario, and the only difference is the location. Outrun on the Genesis was an uglier arcade Outrun, just like GT3 is an uglier GT4. I'm not seeing the point you're trying to make.
Finally, when you say "it's the same game as ever under the hood" I have to wonder why that's a complaint on a shmup site. No, genres aren't going to be completely recycled and replaced every five years, but why should they? Some genres (sports and sims, FPS) benefit hugely from better AI, physics and graphics, some (2D fighters, freeform games) benefit from added amounts of RAM, some (some platformers, GTA and their ilk, Morrowind and its ilk, FPS) benefit from the ability to show absolutely gigantic worlds with little or no loading. These advances are real, and I don't understand why people insist, every generation, that "it can never get better than this." I remember people saying that when the PS2 was about to be released about the PSOne as well... and as a fan of racers, FPS and RPGs (in addition to shmups, platformers and other genres which don't really benefit that much anymore), I can only think back on that viewpoint and laugh.
(no, I don't know why every reply of mine winds up being a novel

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