Is Tsumugi Kotobuki more than she appears

Is Tsumugi Kotobuki more than she appears? is a video on the timtam 2400 YouTube channel.
== Description ==
Why has it taken us so long to figure it out? Mugi has always been a bit on the weird side.
== Transcript ==
Tsumugi Kotobuki. Arguably K-On!'s strangest character. There is no one else in the show quite like her. I'd say the thing that sticks out most is her seemingly impossible strength. Most teenage girls shouldn't be able to do what Mugi can. It's really strange. And as far as I know, she's the only blonde in the show. Maybe it's because she's blonde that she's so strong? And despite being quite polite and gentle, she can be quite a rebel at times. 
Wait a second. Blonde hair, what seems like super strength, rebellious nature. Where have I seen those traits before? Oh my god, could it be—could it be that Mugi, sweet and gentle yet ditzy Mugi, is actually a Super Saiyan? I don't believe it. Why has no one made the connection yet? It makes so much sense. Maybe the girl that we K-On! fans have grown to love who wouldn't hurt a fly is actually the first ever female Super Saiyan. It all adds up. We've just never thought to put the pieces together. 
Let's think about this. No other character in K-On! is like Mugi. All the signs in the show points towards her being the legendary Super Saiyan. It does explain a lot about her. Oh, but Tim, that's impossible. Where's the spiky hair? Where's the tail? She never flies or shoots energy blasts either. Valid points, yes, but maybe that's because of what K-On! is. Cute girls doing cute things. If Mugi did do the stuff from DBZ, most people wouldn't consider it cute. 
Let's go through the various facts and whatnot. As we all know, a Saiyan's hair goes blonde when they go super. Mugi has blonde hair. "But it's not spiky. And all her eyes must go green as well." I think her family has something to do with that. Remember, Mugi comes from a rich family. Since they're rich, it is entirely possible that they can use that money to buy resources. Scientific resources. Don't forget, we have not yet seen a female Super Saiyan, at least not canonically. Maybe Mugi was an attempt at creating one. An experiment. We all know that experiments can fail. Maybe the Kotobuki scientists got the color of her hair right, but they couldn't get the style. "Okay, but wouldn't she change back to normal eventually? A Saiyan can't stay super forever." 
Think back to the Hyperbolic Time Chamber. What is it that Goku and Gohan did? ["Somehow, we have to get to a point where it feels natural to be a Super Saiyan, so that we can stay like that all the time."] What's not to say that Mugi isn't secretly training like they did. Working on mastering the first Super Saiyan form so she can stay that way for long periods of time. Remember when she went to Finland? Maybe the holiday was actually just a cover story. Maybe the staff of the Kotobuki family are aware of what Mugi really is, but they've been sworn into secrecy. 
"Boy, but is she really that strong?" Have you not seen the show? Do you remember this? [clip "There's not a bead of sweat on her!"] Or this? [Let me give it a try." "I have avenged your honor, Ricchan."] Let's see that again in slow motion. [clip] And that machine was on maximum setting. How many teenage girls do you know who can do that? And the K-On! Wikia specifically states that she regularly runs at a brisk jog with her instrument, the cork triton synthesizer, slung across her shoulder. And last I checked, that keyboard was said to be pretty heavy. And while we're at it, if you think back to the movie, she was running with not only her keyboard, but 30 kgs of luggage as well, without getting tired. And before you mention the pillow fight, Mugi would have had to hold back, lest she decides to take Mio's head clean off. 
"What about the tail then? Don't Saiyans have tails? Remember Goten and Trunks?" It is entirely possible that when they were born they had tails, which would have been removed. Another possibility? The Kotubuki scientists left that detail out. "Okay, but you said earlier that Mugi is a bit of a rebel. How can she be a rebel?" You're forgetting about someone very important. Vegeta. You'll notice that he has been shown to be a rebel a number of times. He does what he wants, when he wants, and he doesn't let anyone tell him what to do. Sure, he's not originally from a rich family, but my point still stands. And if I again make quotes from the K-On! Wikia, Mugi displays a rebellious streak occasionally due to her wanting to deviate from her wealthy nature and diverts from a well-behaved and matured demeanor to the surprise of others. And, lest we all forget. [Mugi eats Mio's strawberry clip]
So, I think I've covered all the bases. Mugi must actually be a Super Saiyan. There's too much evidence to dismiss this. Maybe she was actually a rejected character for DBZ. They drew her, but decided she was too cutesy, so she got put into K-On!. And what was her childhood dream in Ura-On!? [When I Grow Up "Conquer the World"...] So, Mugi-chan, what do you have to say to all of this?