I like old systems (80s/begin 90s non PC hardware) because you can understand them completely from the silicon level up. I have begin 80s systems which I know everything about on hardware and software level, which is a lot of fun (at least to me). I can read the OS code and understand and remember it; try that with win/lin/mac. I can remember (to enough detail) all the hardware layout, and, without any documentation, solder in more memory.
I think the question 'what is the use?' is akin to asking what the use is of many/most hobbies; it is a way to relax while getting intellectually stimulated. If I would do that with modern computers, the idea of 'maybe this can make money!' immediately jumps in my head and the nice, relaxed atmosphere is gone. I think it's a hobby for many and not a bad one at that. Ohyeah, and then I (and many with me) am weird; I think ps4/xbox one games generally suck; give me Metal Gear I or Nemesis-2 on the MSX-2 any time over those overrated graphical jerk off sessions (disclaimer: I have all PSs, to me they got gradually worse, game wise; more Crash, less FPS crap please). But that's a matter of taste.
Remember the feeling when you had your first bicycle? Can you get it again from another bicycle like that?
(Heraclitus' river, etc. Just trying to explain, the rest of your post is quite fair.)
I'm pretty sure the answer is yes. I loved the Amiga for what it was, but it's hard to see why anyone would get a "modern Amiga" for any reason other than to say that they had a "modern Amiga." I don't think any Amiga has shipped in quantity since the Amiga 4000 in 1996; I don't know if it's fair to say that the PowerPC-based designs were obsolete before they shipped, but I don't know that it's unfair, either. (The X1000 became available in 2012, using a CPU that was released in 2007 and will never be updated again.) I could imagine someone whose business still depended on Amiga-specific software getting new hardware back in 2000, but 2014?
Personally, my nostalgia for old computers tends to last roughly long enough for me to download an emulator, get whatever virtual machine I'm trying to emulate working, and be disappointed. A computer may have been years ahead of its time for the late 1980s, but it'll likely still feel like banging rocks together in the mid 2010s.