The older I got, the more I appreciated how cool the Archimedes could be (especially after seeing Zarch which I think was more technically impressive than anything on the Amiga 500 at the time - I might be exaggerating), but it was a rare and strange beast mostly seen in school IT departments, and the teachers even then tended to be quite protective of the expensive machines.
Being as it was a relative of the BBC Microcomputer, it would always have been an uphill struggle to win the hearts of school kids wearing their parents' wallets down at Christmas time, and was anyway a lot more expensive.
Everyone had Amigas because there was a very healthy Euro/Global trade in pirated games from crackers on BBS' - Amiga had an ecosystem useful to schoolkids, Archimedes did not.
That said - I too would love to have a peek at an alternate timeline! I distinctly remember sitting as an UnMin in Gatwick airport reading some Acorn computer magazine heralding the new age of the Archimedes and getting quite excited. Oh well.
- ed
additionally - I think the demo scene tended to be very tightly wrapped into the cracker/pirate scene, ie. they were pretty much one and the same.