There's just something uniquely special about hand-drawn pixel art at resolutions around 320 x 200 with 16 to 256 colors - especially when viewed on analog CRT screens with their scanlines and phosphor glow which blend colors and soften the hard pixel edges some people today think as "retro" (which isn't at all how this art actually looked in the 80s to the artists or their audiences).
I think a key aspect of the magic is that the technical constraints force art to be representational instead of photo realistic. There just weren't enough pixels or colors, so artists had to make intentional choices about where to focus their limited pixels and palette to imply the detail they couldn't fully draw and that made their images evocative in ways photo-realism usually isn't. Earlier digital graphics with 4 to 16 colors and resolutions around 160 x 120 to were generally 'moving icons' as seen in arcade games like Pac-Man, Donkey Kong and Galaga and most late-70s and early 80s home computers (Apple II, Atari 400/800, C64, etc). Of course, this wasn't just due to pixel and palette limitations but also the 8-bit CPUs at sub-4 MHz clock speeds and limited memory (usually 8k to 32k game size).
It wasn't until around the mid-80s when arcade and personal computer hardware with 16-bit CPUs at 8 Mhz+ and 256K memory hit that magic middle-ground we see as unique to that era of computer and arcade graphics. By the mid-90s it was already starting to vanish as palettes grew beyond 256 colors and resolutions exceeded 15Khz analog video (roughly 240 lines high). A great example of the peak visuals possible from the painstaking care and artistic virtuosity of this era can be seen in the incredible hand-drawn sprites of "Street Fighter II": https://fabiensanglard.net/sf2_sheets/index.html.
The other reason I think so many of us see the art style of this era as uniquely special is it ended suddenly with a huge leap to deep color palettes, higher resolutions and 3D rendered graphics. This happened due to the unique nature of analog 15Khz video and the desire to avoid interlace flicker, causing resolutions for most consumer-priced computers and game consoles to max out in the mid-80s at less than 240 vertical lines. Since artists generally want to work in roughly square pixels, this limits horizontal resolution to around 320. So, for nearly a decade the benefits of using the existing televisions consumers already had, limited the visual output of home computers and game consoles to 240 lines. It even froze the evolution of most arcade machines due to the cost savings of using CRTs made for TVs. Even one of the last 2D arcade hardware platforms, Capcom's 1996 CPS III, was limited to 384 x 224 resolution. After this unprecedented 'hold' of nearly ten years on the march of pixel progress, the next increment most consumers saw was a huge and seemingly sudden leap - a doubling of vertical and horizontal resolutions and a jump from 4 and 8-bit palettes (16 to 256 colors) straight to 16-bit palettes (65,535 colors). And this happened at almost the same moment the rush to 3D rendered graphics killed any interest in hand-drawn pixels. In just a few years, virtually all the computer and game pixels consumers saw changed dramatically in both scope and style, creating a clear divide between hand-drawn 2D pixel art at analog resolutions and everything that came after.