This whole situation is insane.
Let's take the game as-is: Miis can be used in-game with any size, any weight, any moveset at anytime. There is no way to change that from the game ever ; to do that you need to add external rules, and any of those has to be thoroughly justified with precise competitive reasoning and proofs behind (ex: sudden death not played).
Most people agree for various reasons (mainly logistics) that size and weight should be standardized. Guests Miis are generally accepted for that. That's already a major loss of flexibility and liberty compared to what the game has to offer, but it's mostly fine.
Then it can be argued that being able to counterpick moves between matches is a supplemental/"unfair" advantage to Miis, since with only one character a player has a lot more flexibility against various MUs. Fine, MLG provided a simple but efficient solution to this problem by limiting only one moveset (per type of Mii) per set. Nobody complained.
Point is : we are already talking about a compromise. Don't act as if Mii players don't want to let go anything related to their character, because that's not the case. Yeah they don't want to let go the choice of moveset, because you know that's about the main reason the character was designed in the first place, and his main specificity built in the game core. But they are ready to drop literally everything else for that.
MLG rules (1 moveset per set standard size/weight) were great, because it was a real and comprehensive middle-ground, providing a good sentiment of "fairness" while still being in line with how the game works. Problems were solved with just what was needed, no more, no less. (Note that even when everyone seemed happy with their rules and the event itself ran fine, no other major did the same thing after that. Biais anyone ?)
So with the MLG restrictions in mind, let's try to decrypt what different people really want with all those "meta" thing.
Some people want a "custom: off" meta.
Aka "unless proven necessary [which requires testing], we only use ingame settings and turn customs to off, and thus Miis can choose their moveset". Aka "Miis do not have regular customs, because the game itself says so". Aka "we do not want special treatment by tournament rules, but the exact opposite". Aka "turn the game on and leave us f*cking alone".
I do not think any competitive problem has arisen from such a ruleset (see MLG), and it produces nothing buggy, time-consuming or over-centralizing that could hamper a tournament. Consequently, there is no need for an additional rule. Simpler is better.
Some people want a "no customization" meta.
Aka "Miis are custom characters that require to go to a customization menu to be created, and thus are completely banned". Obviously that's not what the vast majority of people want (removing three whole characters from a competitive fighting game is huge), but at least there is some logical reasoning as to why one can want that. No customization and that's all, no exception.
Some people want a "1111 only" meta.
Now is where it gets tricky. First things first : it makes absolutely no sense to talk about a "1111 character" when the custom setting is set to off. We never talk about a 1111 Mario in Melee or Brawl, simply because there isn't any possible alternative. The same way when customs are turned off, it makes no sense to talk about a "1111 Mario", because any other option (ex: 3212 Mario) doesn't even exist in the first place. It's just Mario. The one time we can legitimately talk about a 1111 character is for Miis, because again, they are a built-in special case. But I guess you will simply relegate that to semantics with a wave of your hand, so oh well.
Next, the big question : which need exactly required to add such a restriction ? Just because it's pretty visually ? To piss off Sakurai ? Or an actual, major problem at a national tournament ? How is the simple fact to be able to "not be 1111" an actual polarizing advantage ? How can you even pretend that this is the "default" when you already went by the general customization menus, are in this particular Mii customization sub-menu, the option to modify his special moves is displayed on-screen, and you have to confirm and save all of those for the Mii to even be created ? Including the fact that the game itself doesn't even care about that in the CSS (a Mii is a Mii), and that Miis have a separate customization sub-menu from other characters, further confirming that they are not the same ?
Even a 100%-free-Mii never proved to be problematic, so with MLG rules added I doubt it will ever happen (let's try). We are a competitive community (growing e-sport) driven by competitive values, and the inner workings of the game we are playing have a greater level of authority than your personal opinion. Prove with actual data that your rule is truly necessary to the competitive future of the game, and that you don't just want it because of a misguided and illusory sentiment of fairness due to 4 digits.
[Edit: As pointed by 19_, maybe you deem "unfair" the fact that a Mii player can still create a tailored moveset after the first match, thus providing both an advantage for the Mii player (greater adaptation) and a disadvantage for the opponent (not knowing in advance what the opponent can choose) ? Well, I do not necessarily agree, but even then we can state that "if a Mii is to be used, it should be created at the beginning of the set only". Problem solved, still without the need of restricting the moves themselves.]
And, some people want a "only one pre-determined set" meta.
Technically, maybe this rule will lead to less complains than a "1111 only" one, but logically speaking that's truly awful. Last year with AA's custom project, it took months of discussions to determine the best sets for each character, and in the end there was still upsets. There was ten sets. And now we're supposed to come up with a universally agreed solution with only one ? That's ridiculous.
But even then, do you include size and weight in this unique set ? This will cause more debates (on both sides). What will be the frequency of future updates (if there are any), monitored by which authority (if there are any) ? Who is in charge of creating/transferring them on each and every tournament setup, TOs ? I doubt any of them would be happy to. It's way simpler to let players create their Mii as they play, but if you do that you win 0 second compared to a free moveset. A 3DS = potential delays + who will verify if the uploaded Mii is really "legal" ? Not to mention that a lambda local Mii player will basically be unable to play the character he wants, possibly forever, with no other reason that "some guys on the other side of the world decided you have to play that way" (because let's be realistic, such a rule will be mindlessly copy-pasted everywhere). You will gain complaints for sure, and maybe lose players.
But the best part is that by that rule, you're implying that "special number 1" is not necessarily the default anymore. Which in itself is good and all, but even when admitting that there is no default value, you still want to arbitrarily impose one, for no other reason than… For what already ? It's not for the simplicity of logistics, as demonstrated. If you are afraid of the "unfair" advantage of a greater flexibility of Miis against MUs between matches, then MLG resolved the problem much more simply. If you are afraid of learning more potential (but rare) matchups yourself, then this is a sh*tty reason : it's a competition with money on the line. If you do not want to learn, someone else will, and he will have rightfully earned his advantage against you. So again, why is that rule necessary, and what are its benefits except for shutting up (a little) Mii players by throwing a bone at them ?
TL;DR
Miis do not have regular customs ; they are intended fully-customizable characters and you should deal with it. We are a competitive community, the law is dictated by the game unless we have a valid reason to go against it. Learn to know what meta you really want, and more importantly why you want it. MLG rules were great for everyone because they were a real comprehensive middle-ground, and not an arbitrary one-sided decision. And the event ran fine. The problem is not what the Mii players want, but the unneeded rules that others/influential members of the community/those in power want to impose to them.