Here's what I think:
Why do we allow the loser to change character or stage on MK9? Because we have to make sure that he didn't lose due to the character or the stage. We want to make sure that the winner of that round is the best of the two players, so we lock him and see what happens. Now the loser knows a little bit about his game, so he can play more confidently. If the winner changes his move set, if he gets some new tools, the loser will find himself on that same guessing situation again, so maybe he loses just because he needed some time to warm up. Why would we allow the loser to change character, variation, or stage in MKX? Why would we lock the winner's character and variation? For the same reason. Changing variation is modifying the equation, perhaps on our favor, perhaps not. The move set changes, perhaps not as much as if we changed character, but it is a significant change, anyway.
I think changing variations in the middle of a match is not the point of variations. The point is being able to stay loyal to a certain character. If I want to use Sub-Zero against everyone, for instance, I learn his three variations, instead of learning three different characters. That way, everyone can remain loyal to his favorite. That doesn't mean you have to change your moves after each round just so you can confuse your opponent a little more. Just because the name, look and background of your character remain the same, it doesn't mean that you're not changing anything significant. I think competitive play has to be as far from random as it can. It's our duty to reduce chance and make sure that only the best come out as winners.
On the other hand, if you want to allow the counter-picking game to go a little bit further than it used to go, then you start evaluating players for their ability to read the mind of their opponents on the character select screen as well, and not just the way they play each other on the arena. It's another way of deciding who's best. I'm not saying it's wrong, it's just different.