Isn't stance switch there so they can have characters' fronts and backs look different? and for the xray/super move?
Not sure.
It's a by-product of the animation system. In Street Fighter and lots of other 2D games, the character's front will always be facing the screen. Regardless of what move gets done, the end result is that the reset back to neutral has their front facing the screen. MK9 and Injustice do not enforce this rule. Assuming the character starts with their front facing the screen, a punch that causes them to step forward with their "back" leg will more than likely result in that back leg now being the front leg and the character's neutral stance having their back to the screen. There's no set pattern as to which moves cause a stance switch - it seems to be purely based on visual asthetic and is one of the reasons Injustice and MKX looks so smooth as there's no need to force everyone back into front-facing stances. This obviously applied in MK9 as well but it has quite stiff animations (which IMO were a deliberate throw-back to MK1-Trilogy).
Easy example: Superman's f2 has him step forward and punch with his back-hand. The end result of this is Superman goes from front-facing to back-facing (or vice-versa). However, f23 puts him front-facing again as the second punch (the 3) does a similar thing - attacking with what is now the "back" arm and stepping through.
As for why they actually added a button to just change between the stances, my guess would be 1) to show off the new fluid MK9 animation system, 2) some kind of fake-out move that isn't tea-bagging, 3) because they knew about stance-specific combos (that one is a joke) or 4) it was probably #1.
Speaking of stance-specific combos, as a guess I would say that the hitboxes are 3D and not being projected onto a 2D plane correctly (if they're being projected at all) before the collision checks are made.
