I had the opposite reaction. As someone who was on team PSX, the wobbly jank is pleasingly nostalgic. Didn't someone say that the limitations and artifacts of the obsolete media of the past become the sought-after aesthetics of the future?
This is all subjective so I suppose I should add an IMO, Even back then many games were preferable on the N64 like megaman legends, what the PS1 offered that was superior was storage, which allowed for more music and FMVs, and also allowed for voice acting and probably why MGS is still talked about to this day, my guess is the lack of detail helps immersion the same way you would read a novel, and I imagine the PS1 with its storage would've been the perfect vehicle for Visual Novels, but that still is not popular anywhere but Japan.
Even with realism, ports to dreamcast were better overall and considering the latest port of Final Fantasy Tactics does not emulate any of its PS1 limitations, I don't think a lot of people strive/like the aesthetic.
As someone who was team N64 I do agree PSX has more of a "trademark look" compared to the N64 which is pretty much just a very limited version of a modern graphics rasterizer.
They are certainly sometimes a key part of the retro look that makes things nostalgic.
But even during the PSX era I found it distracting and annoying to look at so I can't say I have any nostalgia for it even now in the way I do for N64-style low-poly 3-D games or good pixel art.