The original Mega Drive Pad didn't work with Amiga, but later they modified it (added some extra wires in the port) and they worked fine with Amigas, also Ataris, C64 and C128s. I think Sega or the pads manufacturer made the decision to add the extra compatibilities to sell more joypads on alien (competitive) markets. I remember having Mega Drive pads which didn't work on Amiga but worked fine with the Sega Mega Drive. The non working pads needed some rewiring to work on Amiga, and as an extra feature I used 3 buttons, but not the Hired Guns A - button. First was the standard Fire button. Second was the Fire 2 button, mostly used by me in Turrican games. And the third button I simply attached it to the wire of the Up and I had a jump button, which is not real third button, but very good for Platforms games, to jump with it.
The Amiga was designed by some of the original Atari 2600 team, and Atari 2600 joysticks in fact work fine on Amiga, but it was already outdated in 1985. Having only 1 button on the Joystick/Joypad is stupid and many Amiga games sucked because of this. I think 2 or 3 buttons Joystick should be set as standard for Amiga, back in 1985. I remember many people preferred to play on the Sega Mega Drive or even NES because the games there supported more buttons and were much more easy and enjoyable to play.