Given each hand has a separate action, they must be. Early controllers like on the 2600 had the button on the left side, with the intend to use the main hand to control the character on screen (the action button was often unused, or used without critical timing). Plenty of third party controllers had the button on the stick itself, so that the main hand was the only hand used, or had a button on both sides of the switch with the same function to accommodate for handedness. It was switched around by Nintendo when controls got more complex with several buttons, to allow the main hand to control the action while the off hand controls the movements. A point to be made is that the dpad thumb is always on the dpad and only need to be pushed around, requiring less fine control than the button finger which is hovering over the buttons and needs to hit the correct button with precise timing. Some early controllers from that era still had buttons on the left side, like the notorious Master System Control Stick. Early console shooters, like Halo, had a lefty control option that switched the sticks so that fine aiming control could be given to the dominant hand, until lazy designers gave up giving options to the player.
As a lefty I don't feel left out by digital controllers like the NES one, controls are simple enough that even the off hand can do a good job with it. And I'm too old to relearn everything mirrored. However I'm shit at console FPS, I just can't aim for the life of me, and that may be why. Same for twin stick shooters like Geometry Wars, I can dodge just fine but shooting isn't my strong point. Maybe I'm just shit at these games and my handedness has nothing to do with it though. Shmups are controlled with the left hand mainly, and I'm not a top player in those either.
The problem with the Goofy Foot controller is that it isn't a mirror image, B and A aren't in the same position relatively to the thumb and that's a big problem for games where you need to hit both or hold one.