The flip stance button(mapped from 3+4) is used to do XRays. If the flip stance button were to be a button of its own without being a 3+4 shortcut, your suggestion would work. But seeing as it is like it is, cancelling into other moves from a 3+4 run would be weird.
Obviously all of this is a moot point because a Run button isn't incorporated, so our conversation is strictly hypothetical. That said, I think you're not looking at it from the point of view of MK being a 6 button game, which is what I'm trying to explain.
Let's assume that in MK9, Flip Stance was "Button 6"
Likewise, let's also label the additional macro buttons like this:
Flip Stance: 6
Throw: 7
Tag: 8
Both the PS3/4 and Xbox 360/One have 4 face buttons, 4 top buttons, and 2 buttons mapped to the click of the thumbsticks, totaling 10 usable in-game buttons for a standard system pad.
Most fightsticks have either 6 or 8 usable in-game buttons. (MK specific sticks have 6, Sanwa style usually have 8)
Let's go with the lowest common denominator, of 6 usable in-game buttons.
MK9 Layout
Front Punch 1
Back Punch 2
Front Kick 3
Back Kick 4
Block 5
Flip Stance 6 (3+4 macro)
Throw 7 (1+3 macro) (pad/sanwa stick only)
Tag 8 (pad/sanwa stick only)
Xray FS+Block OR 3+4+5
Proposed MKX Layout with run button
Front Punch 1
Back Punch 2
Front Kick 3
Back Kick 4
Block 5
Run 6
Throw 7 (1+3 macro) (pad/sanwa stick only)
Flip Stance 8 (3+4 macro) (pad/sanwa stick only)
Xray FS+Block OR 3+4+5
Currently, the ONLY reason that Flip Stance exists is either for aesthetic purposes (Some people don't want their fighter's back to the screen, I guess), or, more importantly, as an Xray "enabler". Think about it, without Flip Stance, Xray is the block button, which you simply can't have. Instead, the flip stance button is used to "enable" the xray.
-If Tag mode isn't in the game, then the button is useless.
-Throw could be mapped to a thumbstick click or you can still mash 1+3 for a throw, it's not hard.
-Flip stance could be omitted entirely and just make Xray it's own button with a macro of 3+4+5
This is how you can make a Run button work. Again, all hypothetical and moot, but also since almost none of us have played the game, it's entirely possible that the way a run button would work, simply wouldn't work with the game's mechanics.