So, there's more than one answer. When it came out the idea was, and it's debatable how much Nintendo used this concept as a marketing tool or with a design in their head, tha the controller allowed flexibility. For different games, different sections or different preferences, you could hold the two outer handles, and get a basic SNES type thing, or you could hold the mid and either one of the sides.

I feel part of it was a bit of mistrust, maybe from some early testing or internal, about the accuracy or the familiarity of users with the joystick, the design allows people to opt into it or go for the tradizional buttons.

I recall some weird stuff was supposed to be meant for the full left side combo, so directional buttons + analog stick. That was a bit of a far reach...

So beside all the intentions, 99% of the games were played with your left hand on the middle handle and the right hand on the righ handle. Consider there's a very comfy trigger button below the middle handle that is mirrored or mirrors the left shoulder button.