I didn't mention Might Final Fight because while the NES original game is a brilliant game, it has lots of limitations when compared to other games of the genre, and also play a lot different. The TMNT game and Streets of Rage I mentioned above are more "traditional" games on the genre. But yeah, it's a great example too.
Like McGeezer said, I am pretty sure that TMNT 3 game could be made on Amiga with more bobs and no flicker like the NES one has
But we didn't have Konami or Sega making games on Amiga.
The major problem wasn't competent coders, but people who actually could design good games around the hardware. Well, good beat'em ups at least.
I'll never forget Richard Applin saying he didn't understand the appeal of games like Double Dragon 2 and Final Fight, and that he preferred playing Shinobi. No wonder his Shinobi port for the Amstrad was great, while Final Fight on Amiga was.. erm... and Double Dragon 2 has lots of gameplay issues (even though technically its great - also running on 512 kb afaik). He didn't understand those games and couldn't transfer the gameplay aspects of them that made them good games on the arcades. (And probably why he thought mantaining the big sprites of Final Fight was more important than, say, keeping all player moves intact)
That's the main point I think. People trying to do beat'em ups without understanding what makes them good on the first place. Last Action Hero is technically very good, but the gameplay stinks. From that engine someone could tweak it and make a very solid beat'em up.
Konami or Capcom could make a great beat'em up running on an OCS 512 kb machine, I am pretty sure