Interesting idea but I think if you consider the way NRS designed MKX in the first place it's pretty silly. Think about it; the variation system is designed to literally change the way you play a character while still keeping their basic move set the same, this is the entire point of the system. What I'm saying is that if you decided to give people the option to change variations mid match you might as well just go the classic fighting game design route and just make single characters without variations. I mean the whole thing just seems counter-intuitive to what the variation system is designed to do in the first place, variations are meant to change how a character plays but you want to pseudo combine them? Also it would unbalance this game even more than it already is (which is not too bad right now, not perfect though), I mean think about all the characters in this game that have three "viable" variations like, Jax, Sonya, Takeda etc and then characters who are only considered to have two or one "viable" variations like Scorpion, Sub-Zero, Kung Lao, Kenshi, etc. You are objectively more powerful by picking a character with more good variations than one with only one or two.
To be honest I think that it would be ridiculous to implement this feature just because of how fighting games are designed in general, especially if you're suggesting a mid game change and not after a round, like seriously the momentum of a match can completely change in a second due to a variation switch, but this is why the game is the way it is now, so that after you lose a match you can go back to character select and swap variations if you want to. You make a choice when the match begins to stick with the variation you chose and I don't like the idea of people getting a "get out of jail free card" just because they built some meter after making a decision to go into what people consider a bad matchup. The only way I could see this being implemented is as a Test Your Luck modifier for fun times but in a serious setting it just seems super counter-intuitive to this games design.