If you've ever wanted to see a useful visualization of thumbstick inversion options, play the game Rock of Ages and check out its control options menu. They have animations of little knights moving wooden joysticks around to demonstrate what the different invert options are like.

Long story short: the non invert options would require a geared joint if they were mechanical apparatuses while invert is simply a stick pointing directly out of the camera's backside.

Personally, I use a bizarre mix of different options depending on the type of camera. I invert Y for first person shooters with a controller, but do not invert with a mouse or when the camera is on a fixed rear axis (where you can't turn around or look in any direction beyond a maximum angle). To make things even more complicated, I like to invert X for third person camera controls, but not for third person aiming controls, though I think that has only come up in the Dead Rising franchise.

People's brains work differently, and it's a simple enough option for devs to implement (certainly simpler than explaining the reasoning), so let's let bygones be bygones.