One thing that strikes me about the Amiga though, despite the superior audio/visual hardware, is how little difference exists between the machines in the visual presentation of most original-era games.
I expect games like Outrun, R-Type or Buggy Boy to be jerky on an ST. But the visuals were similarly bad on the Amiga. I expected better. It's as if the programmers were unable or unwilling to find the time to optimize the code to leverage the Amiga's better graphics hardware. Flight Simulator II, Xenon 2 and Dungeon Master look pretty much identical on both systems.
I'd put that down to harsh deadlines imposed by the games companies on the development teams and not knowing what the Amiga's capabilities were, even though there were books available. The games companies simply wanted to get a product out of the door, cheaply and quickly, and didn't care about the unique abilities of each platform their teams worked on. This mentality is also true of many, many 8-bit ports across the Speccy, C64 and Amstrad at the time, and I suppose most of them didn't develop for the A8 because they saw it as not commercially viable and too difficult to program, with the Display List and everything else.
Other landmark games of the period, such as Lemmings, Sim City, Populous or Frontier just didn't need the ability to push objects around the screen in a manner that would have allowed the Amiga to excel in the visuals.
If you look at the text and interface displays for Lemmings on Amiga, you'll see hi-res graphics used extensively, even with dozens of colours on-screen at once for the messages, all thanks to the Copper. I'd say that's excelling in the visuals for some part.
The Atari 800 got many sub-par conversions of Apple II or Commodore 64 games, but a few games on the Atari 8-bit really demonstrate the graphical difference - games like Dropzone, Boulderdash, Elektraglide or Ballblazer demonstrate a fluidity of motion the 64 just never seemed able to deliver.
The golden age of the A8. Unfortunately, as time went on, they decided that the A8 was not commercially viable because of how expensive the machines were and thus how many fewer users there were, compared to the cheap sales behemoths that were the Big Three, as I call them.
I havn't been able to find many similar examples from the Amiga/ST library where one can say "look, that's why the Amiga is better". Shadow of the Beast is one. What else?
If you stop comparing the Amiga with the ST, then there's all the Team 17 games, as well as many others that actually RTFM and developed solely for Amiga.
Commodore went bankrupt. At a time when the only products in the line-up were Amiga derived. That is a standard definition of a commercial failure.
You can directly blame the Commodore management at the time for that, not the hardware. They had a unique platform that practically landed in their laps, and they didn't know what to do with it. The idiots decided that the Amiga should be used strictly for business (hence the A1000) and leave the gaming to the C64. They were just totally blinkered and wasted time and resources on trying to sell the Amiga as a consumer device like the CDTV or minor hardware updates like the A500+ and A600, and not focus on the Amiga's primary multimedia strengths, which should've been obvious to them. It was a minor miracle that AGA was developed at all (which should've been so much more) despite the management's incompetence and the Commodore design team at the time (and all of us Amiga fans) directly blame Mehdi Ali, the guy at the top, for all of this debacle. Thankfully, other companies developed versatile software and hardware for the Amiga that made it famous in industries like desktop video and gaming, and a lot of Commodore subsidiaries, like the UK, were more successful at promoting the hardware.