I tend to disagree with the "petition", because of obvious balance reasons, but I have to admit that I'd like to see the result of implementing customs variations into tournaments.
Let's take MKX : When you look at the tournaments, most of the time the same variation is picked, obviously the one that is considered as the most powerful : Hollywood/Cassie, Hellfire/Scorpion, GrandMaster/Sub-Zero etc...
But if the system of custom variation was added to MKX, it would be an absolute nightmare to balance. Let's imagine that a custom variation in MKX includes 3 variation-exclusive moves, along with their EX versions, added to the base moveset of a character. I'm not a pro-player, but I'll pick characters that has, in my opinion, at least two tournament viable variations and try to create one extremely powerful variation (I don't remember all the in-game names, but you'll understand anyways) :
Sonya :
1st : Military Stance (Covert Ops)
2nd : Stun grenade
3rd : Grenade reload
Kotal :
1 : OH sword attack
2 : Low sword attack
3 : Obsidian/Crystal totem OR Command Grab (Sun God)
Sub-Zero :
1 : Ice clone
2 : OH hammer (cryomancer)
3 : Command grab (cryomancer)
I could go on, but you understand what I tried to illustrate. My custom variations are probably not optimized, but you got an idea of how it could make the game unplayable. Yes, MKX's variation system is not meant to be tweaked that way, but think about it : Some people think that variations from MKX weren't very interesting because only one was played over the two others most of the time. But, if you let the players picking a custom variation in tournament, people will eventually find the most optimized combination of specials and... almost everybody will use this one. So the problem will remain the same. Some players will say that not including the custom variations would be a missed opportunity, but if this opportunity turns out to be negative on the competitive point of view, that is not a good thing at all, both for the community and NRS. They took the safe choice to exclude custom variations, and I understand it.