Where does this hairstyle originate from?

Of course this hair style is found in a cartoon and thus not really bound to any reality either historically or as mart pointed out in comments physical reality:

I envy the sheer volume of hair these toons must have, to have such full ponytails with mostly shaved heads! – mart

That makes

Where does this hairstyle originate from?

an easy answer: From a childish fantasy. (Note that 'childish' is not an insult here but an ethological concept. )

Therefore, I struggle to read any "It's a…" as correct. Top knot is just a generic description and there are many similar ones now. (List for aficionados)

But if we want to list inspirations for that from real history then we might want to include the

the Sikha,

the Khokhol, or osedelet

Gadao's style,

Manchu warrior style

a korean sangtu similar to a Chinese touji and popular for Göktürks and other Altai people like Mongols historically popular variations

Given the most likely place these shows are actually drawn onto film, it stands as well to reason to suspect the origin in Let's trim our hair in accordance with the socialist lifestyle.
An acceptable example:

Those most commonly associated with almost fanatical shaving were of course the ancient Egyptians, sometimes going bald, with whigs or ponytails still popular in that general vicinity: And of course, Minoans never missed a trend

This style is found around the entire world and throughout much of histoy and even before that.

It might be argued that iron age Irish also found a liking to that general style: from the so called Clonycavan Man "the hair of Clonycavan man (Ireland) is shaved at the front and then piled high, set with imported resin"

Some Suebian knots, or Viking or Frankish styles

An Aztec quachichictli as seen on screen with Mayas

Other native American trends like those often associated with Mohicans, Wyandot and Mohawks

This might indicate some connection to "warrior culture", as the style is also repeated in many helmet designs. From Roman Galeas over Avars: to more familiar ones: or an English variant

But interestingly, this top knot/ponytail plume style seems to be quite absent from Japanese helmet designs that mainly use Tatemono. So there are quite a few connections to "warrior", and quite popular through the ages in Asiatic warriors, it is apparently just not that typical for Japanese warriors to shave their heads in the style of "sides bare, top knot up and extending". Apart from budo traditions with the style called chonmage mentioned elsewhere, shaving the head completely has some distinct characteristics: The meaning of shaving head in Japan. But it was for quite a while tradition to shave just the part that's so prominent in the question: the crown.

And then there are of course the almighty fashion gods

The Undercut Bun Aka The Top Knot

the Romford facelift similar to the Croydon facelift as well.

Again, the cartoons, whether in the anime style or what else the other one example is (bulbous blob style?), are not historically accurate, by definition. If we insist on the earliest use of this hairstyle, then it's probably pre-history:

But even this remains speculation:

The topknot is many things; an easy option on a bad hair day, a signature look of the street-style star or what the zeitgeist is now calling the man bun. But few really know the long and storied past of what essentially is a lazy bun. The true origin of it is unknown, but the hairstyle was surely created before Jared Leto and stems across many cultures. So the next time you're feeling trendy in the hairstyle du jour, remember this ‘do has roots.
_{A Telling History of the Topknot—From Samurai to Man Buns}

In the case of Zuko from the first picture, it is probably adequate to assume that this hair style is meant not so much as cultural representation from or allusion to any real history, but that his temporary top knot is more "like a visual expression of his character development" and apart from the possible status and aggressive connotations conveys as much as "that the top knot represents rigidity and restriction".
In anime top knot characters are just a thing:

Anime Hair: A catch-all term used for anime, manga and other cartoon and comic characters with bizarre, improbable, or just plain goofy-looking hairstyles. Usually, the most important characters of the story will have wild spikes or a cool-looking hairdo in order to stand out among the crowd. It also helps to create a distinctive silhouette that will stand out in branding, media, and merchandise. It may be one or more different colors that don't appear naturally in real humans (blue is a popular choice).

Similar for the second example:

Quetches are maybe the most uninteresting species. […] These creatures are little humanoids with an olive-shaped head and a pony tail growing right on top.

They are even less interpretable, as they are all just designed the way they are.

If anyone wants to read a deeper meaning into wearing topknots: The symbolism and meaning of the top knot and the origin of the practice of wearing top knots

It is a pity that the source of this question is so incredibly modern:

Ideas as to what constitutes attractive or appropriate hair have varied throughout the ages. As a result of the survey, religion and social status might be considered to be the two predominant factors that have influenced hairstyle throughout history. However, in Western societies, religion has lost importance, and political and social changes are gradually leveling the differences between social classes. In both Western and Non-European cultures, globalization and mass media are reducing the differences between nations, especially amongst young people. In modern-day societies tending to democracy and westernization, individuality is the prevailing feature of the hairstyle. Since art, sculpture, portraiture, and painting in the classical sense have disappeared, hairstyles in modern society are reflected mainly in products of the film and beauty industries, on television, and all sorts of celebrities and stars.
_{Norbert Haas: "Hair over the Ages and in Art – The Culture, and Social History of Hair and its Depiction in Art", in: David A. Whitting & Ulrike Blume-Peytavi & Antonella Tosti & Ralph M. Trüeb: "Hair Growth and Disorders", Springer: Berlin, Heidelberg, 2008, p 536.}