For the 3DS, it's up in the air.
For the Wii U, no, but probably for logistical reasons more than balance reasons. Pretend that a tourney has 128 people competing in it. Every singe match, players are going to have to change their characters to what they want.
How long is that going to take? Will it be an easy "Mario Fireball A, B, or C" or will it be sliders that change characteristics "Mario Fireball, Speed 20%, Size 30%, Power 50%?" The former could be bearable, but the latter would be a nightmare. Then, consider that tournament players use multiple characters and will have to set them all up.
Let's assume that each moveset is locked to the name of the player (if it isn't then it won't work, since some people will play as the same character). The only practical way to speed along the process is to have a period before the event where players can set up their names ahead of time. That has its problems too. A person could stay at the set-up event for a long time and watch his foes set up to gain an advantage over them while they play blind. If it's a secretive thing done, then who is to say that someone won't screw up a moveset of someone else?
It's just not practical for the Wii U version unless it works like this- people can save their characters on their remote. In Pokemon Battle Revolution, you could save a team onto your Wiimote and then take it to a friend's house and play with that same team on their system. The question is whether that would work for the Pro Controllers or not.
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