Miis are already shafted though compared to the rest of the characters, they're not playable when customization is off. They also don't have their own trailer, art, or logo on the website. Has is be confirmed that move customization is handled on the main select screen? Gear customization too? I feel like there has to be a separate menu for all this stuff.
They had their own trailer, it just isn't on the Smash Bros site, probably because it was part of the E3 presentation and wasn't stand alone. There wasn't a good place to cut it off, as it has all the Amiibo stuff in it and it would be like 10 minutes long.
They don't have an icon because they're unique Smash characters. These Miis haven't appeared in any previous Nintendo game. They don't reference Wii Sports of anything that would associate them with a Mii logo, they're entirely Smash Bros creations. This was explained by Sakurai.
Nobody has ever said they weren't playable with customization off. This is entirely made up and has never been sourced.
Customization for moves and cosmetics are handled on a different menu. But Miis share the same menu as any other character for customization, they don't get a unique "Mii" menu, other than for hats and costumes.