My two cents, for what it's worth...
If the issue is balance, I fail to see what difference it makes allowing custom variations versus presets when players are going to gravitate to the most effective thing available to them in either case. No Scorpion player is going to skip out on Misery Blade -- be it custom or preset -- for example. So why not just give players the ability to decide for themselves?
Again, if the issue is balance, there are more than enough tools available to the developer already to balance the selectable moves. Between multi-slot abilities, abilities overwriting moves in the base kit, and abilities having shared inputs, there are multiple ways to ensure a character can't have the most broken loadout imaginable and that's without even getting into the hard changes like scaling, damage output, etc, that are also possible. So if it were, for example, determined that Kabal having Air Hook and Extended Hook together is overpowered, all they would have to do is make both require 2 slots, or share the same input, or any other number of things they could do that would require a minimal amount of effort on their part.
If the issue is stalling tournament play, there's no reason they can't simply make the custom moves UI accessible from the character select screen. Press 3 to choose your character, cycle through the presets for the costume you want (the presets each have a different skin) and press 2, move selection screen pops up with all three slots empty and select your three (or two depending) choices. Press 3 again, and done. The whole process would take the same amount of time, if not less, than a button check.
If the issue is stalling tournament play due to counter-picking, that exists in a preset environment already. Again, with the above in place, a person deciding to counter-pick will have to go back to character select regardless if the standard is preset or custom and the difference between choosing a preset or a custom with the above change in place would be a matter of seconds.
If the issue is "flying blind" isn't fair, just make the loadouts visible on the loading screen. There you go; problem solved. "Oh, this Kabal is using Low Hook instead of Low Buzzsaw, I'll have to look out for that". Now it's fair. No going in blind.
I see no reason at all that custom variations shouldn't be allowed other than NRS doesn't want to have to put in the extra effort required to make this system shine. It's essentially a gimmick to lure in casual players to generate sales and nothing more. Sad, because the concept in and of itself is an absolutely fantastic idea.