I feel like fundamentally games nowadays are still similar to the 360/PS3 generation of games, just they look and play better for most part. So I find it hard to feel 'nostalgic' about the era when it's kinda just the current era but more shit looking. Certain titles might make me feel nostalgic, like Halo cause I have an emotional connection to those franchises but on a whole eh. Doesn't help that I didn't own a console of the era, so my experience is largely through multi-platform PC games.
The PS2 on the other hand had a massive library and many weird games. Are any developers going to make a weird open world steampunk game where you drive car robots about the place and perform street music for spare change? No. It was a weirder more experimental age, and there were more lower budget and smaller developers making weirder things.
If we go even further back, well 2D pixel art games are also a rarity nowadays. They do exist in the indie space I suppose.