Even at the height of its technical superiority, it was crippled for serious work. Its pixels weren't square in any graphics mode, and in the highest resolution mode you needed to endure flicker unless you had a special monitor.
I remember when our 512k mac's power supply died and we tried to use our (maxed out) Amiga for word processing we discovered the top-rated word processors became unresponsive with documents over 4-5 pages (WriteNow on the Mac was cheerfully handling hundred page documents with graphics). And its print quality was atrocious even setting aside the whole non square pixel problem.
Back then almost everyone was still designing for print, and the Amiga just wasn't cut out for that. It was a multimedia machine before there was any way to distribute multimedia to anyone else than other Amiga users.
Video production was a niche that was compatible with the Amiga's design, but working with analog video wasn't going to be mainstream ever... and for digital video, the Amiga was fundamentally underpowered.
These are the kinds of arguments against the Amiga that I actually heard: "Who would ever need 4096 colors?" "I don't need to use all those sounds" (coming from IBM PC owners whose computers could only display 16 colors and only produce bleeps and blops for sound).
The Amiga's real forte was games, pure and simple. It was a monster of a gaming rig, for the day, and a ton of gaming innovation happened on the platform. Gaming was a pretty mainstream activity for computer users even then, and Commodore completely flopped by not marketing the Amiga as primarily a gaming machine.
What I don't get: Why don't they use at least a customized case which doesn't look like a typical PC case (such as Apple does with the Mac Pro)?