Yes, I've thought that the SNES, and to some degree, the Genesis, is where you can go back and find a lot of stuff in the "normal" line to play that holds up pretty well. I've gotten my kids (7 & 5) to respond to some SNES stuff, but anything earlier they find uncompelling.
I can't entirely disagree.
For context, my first console was an Intellivision, so, no, this is not because my first console was a SNES. I did own one for a while... in the early 21st century, long after the PS2 was established.
I think some of it is just that the limitations of the medium were just so shocking prior to that. The Atari era basically couldn't have text; every text you see on the 2600 is freakishly expensive. The Nintendo era was still counting every letter. The SNES era may still be terribly constrained by modern standards, but at least you could make pictures that were recognizable, play recognizable sounds, use text without too much fear, include more variations in play without too much effort, etc. There's a handful of games prior to that that work miracles with the resources they have (Super Mario 3 isn't "just" a classic, it's legitimately amazing for the hardware).
I'd point out that even the people putatively writing Indie games with "old school aesthetics" almost never hold themselves to the limitations of the Nintendo era or before. There are some games that come reasonably close to SNES aesthetics, though.