I'm mixed when it comes to Miis, on one side, I can have Mario fight Bob Ross. On the other side, you'll see nothing BUT Miis online.
I don't think you would see nothing but Miis online. People would have to give up characters they really like, and likely have a connection to, with some created character who probably has a less interested move-pool and far less character. If anything, the people online using Miis are probably just going to be people who want to troll by creating themed or butt-ugly Miis and messing around.
The way I see it, there are four likely ways they would incorporate the character, if they do so at all:
1. Similar to Mario Kart Wii, break miis up into 'weight' classes based on their size, given a bulky, medium, and lightweight variety of a generic moveset for the character. Small differences in the moves might exist, but ultimately the difference between them would simply be in power vs mobility.
2. Scale all Miis to be the same size, to keep hurtboxes and whatnot consistent, and create an actual unique movepool for the character. This would be the most like its own legitimate character, given consistent hitboxes, moves, power, mobility, etc - the customization of this character would be aesthetic only. The moveset would have to be influenced by things such as Wii Sports, and other similar Wii console references/features.
3. Like many other fighting games, use the Mii to act as a 'clone' or 'mimic' character, completely copying other character's movesets. Similar to Edge Master or Charade in the Soul Calibur series, this type of mimic could change what character they are every stock to differentiate from just choosing Random. I find this to be incredibly unlikely, due to the difficulty in having a Mii mimic the moves of many of the abnormal characters such as Bowser. This is definitely possible though, especially if they get costumes similar to in the Nintendo Land game on Wii U. The Mii also might steal the spotlight from the characters themselves, which Sakurai might not like.
4. Non-playable character. Similar to the multi-man battles, you would instead fight hordes of Miis taken from your console. Similarly, they might just throw a Mii or two in with the new multi-man characters, due to most people not having
that many Miis. Regardless, this option means they would have no special attacks, which I think is more likely than them getting completely unique movepools.
This is definitely a character that I'd need Sakurai's word to believe - whereas Palutena is one that I can believe from a leak. I feel like the Wii Fit Trainer serves more than enough of a roll for what the Mii would be, being a console representative and then some.