I think Amiga find themselves at the perfect border of extendable and retro. Mine has 1024x768 (over hdmi/dvi), 128MB of ram, a cpu almost 5x faster than it shipped with (66MHz vs 14MHz), and an ethernet (pcmcia) card. I don't have usb yet, but it's possible. I also have unreasonable amounts of storage (compared to the design) via an sdcard.
Much older and you lose all of this. Much newer, and you just end up replacing a PC with a crap PC.
Retro computing is a hobby. People generally like their hobbies. Like, why do people like old cars? There are better cars out there but some people are attracted to them.
Amiga was a computer that was way ahead of its time with its hardware AND software and provided so much fun until it was deemed obsolete - and it was a long time. Nothing like that existed for a long long time. But all of it doesn't matter - it is like the classic car analogy, it is just a hobby of some people, to reminisce on their childhood etc.
>challenge to make it do something it couldn't do
This is another hobby altogether. You can do it with retro computers, or with modern computers and artificial limitations (think of the demoscene and their 4k or 64k competitions) and actually this mindset does not even require a computer. Making things do things they are not supposed to do is just a fun time for some people, a creative outlet.
The thing I find interesting about retro computing is how far one can take the platform in terms of productivity. In other words, how far can the platform be taken if one ignores content consumption.
There's also a minimalists/efficiency mindset at play. If I confine youtube to the living room, can I satisfy my daily desktop needs with an older system? Is that older system actually faster (because of less software bloat) even though it's running on much more constrained hardware? Do I actually need an operating system that supports multiple logged in users for my desktop use cases? Are modern UIs more distracting and actually an impediment on productivity?
I can't speak for others but these questions are interesting to me.
I have an DEC VT320 terminal hooked to one of my Linux machines, and when I need to heads down, no distractions, pound out text, I pull it into a room without a computer (or TV) and close the door. It's a great way to block out distractions. George RR Martin famously writes his books in Wordstar on a DOS PC not connected to the Internet for similar reasons.
The big limiting factor with using a vintage computer for a daily driver is that very few of them have a browser that supports modern web standards, have relatively low resolution screens and are painfully slow doing modern crypto (TLS & SSH), so much of the modern internet is inaccessible or unusable.
For me, almost purely nostalgia. As silly as it sounds, meeting goals I set for myself when I was 12. (Plus a sprinkling of convenience; the scan-doubler lets me use a leftover flatscreen instead of a hulking CRT, ethernet saves me a lot of heartache transferring files from my desktop, etc).
But mostly just games. I didn't really play games from roughly 1995-2010 for various reasons, so Amiga (and megadrive) are still where a lot of my old favourites are. Thanks to Catalina, my desktop can't play civ5 anymore. But my Amiga can still play civ1!
Much older and you lose all of this. Much newer, and you just end up replacing a PC with a crap PC.