Rather than edit myself again, nnh... I should mention I got my start on/with Tandy myself, though that was a 1000SX, so the whole CoCo scene kind of blew under my radar until it was Too Late. So I definitely think that 'forgotten' scene deserves credit where credit is due, too.
But to explain where I think the Amiga truly and maybe-if-we're-lucky-undeniably fits in... Look at what you got in the box: Computer. Multitasking OS with a windowing environment. 2-button mouse.
Flip ahead 10, 15, 20 years. You go out to buy "a computer." What do you get in the box? Computer. Multitasking OS with a windowing environment. 2-button mouse. (Unless you're an Apple diehard, anyway.)
Look at the way you interacted with the machine -- GUI for most of it, CLI for some of it. Look at the software you ran on it. The "interaction model" didn't undergo many drastic changes. Sure, the menus and screens are a little weird, but not nearly as weird as the shift Microsoft's platform underwent going from "3.x" to "95," or *NIX systems underwent trying to settle on whether "desktop environments" were even a good idea.
The sheer concept that you'd be sitting here with iTunes or WinAMP or XMMS or, um, Prayer? blaring while posting to Amiga.org from software running in a window, then knocking off to play some Quake or something full-screen? That the boundaries of the human interface were going to be drawn that way -- consistency for some things, skins and full-screen for others, and a constant squabble over which is better? Well, yeah, from the moment you saw the Mac, you might've been thinking along those lines, but Commodore got to be the first ones to cram that possibility in cardboard and slap a price tag on it.
OS-9 gets "multitasking," but I'm pretty sure Amiga gets "first consumer product to present what would become dominant paradigms for normal humans interacting with a multitasking system," for better or worse, and however exciting that is. Could anyone have possibly planned this? I dunno, but who knew sliding a puck around and pointing at virtual sheets of paper was going to become universally-accepted in the first place?
[Now if anyone knows how to convey *that* distinction succinctly, let me know.]
[Edit: Yaargh, and in cleaning that up before submitting, I did leave off the basic question: OS-9 didn't have a desktop/Finder/Workbench equivalent until after the Mac and Amiga had launched, riiight? I have the dim and possibly-incorrect concept that it was more oriented around virtual terminals or something like, but I also have a similarly vague memory that something 'windowy' or 'Finderesque' was available by the time TRS gave up the line. :-?]