In anime, most women are shown to be housewives. Even in romantic comedies, girls dream to be a good housewife after they marry their boyfriends. Very few are shown to be working, and even if they are shown, they are portrayed as poor mothers, e.g. Nisekoi.
Why is it so? Why do they finally become submissive towards the end of the story? I haven't seen "many" girls in anime aspiring to be live independently.
TLDR: The premise of the question is only true for male-oriented works.
The main bulk of the question (the reason for women in anime being portrayed mainly as housewives) has been answered by Fumikage Tokoyami quite comprehensively, so this is more of a frame challenge to the question than a straight answer.
There is significant gap between the portrayal of women in anime/manga between male- and female- oriented works. In male-oriented works, female characters do indeed frequently end up as full-time housewives or at least dream of becoming one – however, this really is not the case in shoujo (works targeting girls) or josei (works targeting adult women).
Even in romantic comedies, girls dream to be a good housewife after they marry their boyfriends. Very few are shown to be working, and even if they are shown, they are portrayed as poor mothers, e.g. Nisekoi.
Note that Nisekoi is shounen (and a harem comedy, the most male-wish-fulfillment style of romantic comedy at that). In shoujo, if the future beyond school/university is mentioned at all, female characters will very frequently (if not almost always) have concrete career goals, and will be shown achieving them if the story does progress that far (e.g. Yukino becoming a plastic surgeon in Karekano, Shizuku passing the bar exam in Tonari no Kaibutsu-kun, Koizumi Lisa wanting to become a stylist in Lovely Complex)
In Josei (targeting adult women), this is even more apparent – very rarely will the main female lead not have a career (see Nodame Cantabile, any of Nishi Keiko’s works, Natsuyuki Rendezvous and so on) In fact, the stereotypical Josei romance plot could be summed up as: Careerwoman tired of her job and life in general meets handsome man romantically interested in her – hijinks ensue.
The example of Hinata Hyuga (as given by Fumikage Tokoyami in their answer before their edit) and the ending of Naruto in general is interesting, because the major female characters, with veritable abilities and merits, end up as domestic supporters for the male characters, rather than holding significant positions of their own. This kind of “sudden housewife” shift (or as the OP put it, "become submissive towards the end of the story”, is almost exclusive to shounen or seinen.
In shoujo or josei, characters who appear mainly as housewives or in an otherwise domestic role will generally start out enjoying or showing interest in such roles (e.g. Love So Life – the female lead of which does dream of becoming a nursery teacher), at least disillusionment or a lack of interest in her career (e,g, side characters in Nishi Keiko’s works, Nigeru wa haji daga, yaku ni tatsu – the female lead here does end up working again, IIRC) or as a mother of a main character.
In short, the idea that most women in anime are housewives (or aim to be housewives) is for the most part a phenomenon limited to male-oriented works. The situation for female characters in female-oriented works is much more complex.
Sidenote: That said, many shoujo and josei works DO end up in marriage – While there certainly are exceptions like & (that’s the title), it can be deduced that marriage is still considered important, as Fumikage Tokoyami has stated.
Since the question has picked up steam, I am going to construct the answer by including both historical and modern viewpoint and then the depiction of women in anime and manga
The proper name for the trope is Yamato Nadeshiko. "Yamato" is one of the older, fancier and more poetic name for Japan and the Japanese people. "Nadeshiko" is the Japanese name for Dianthus superbus, a wildflower found in the Japanese highlands that is related to the carnation (Dianthus caryophyllus). So, taken together, "Yamado Nadeshiko" is used to mean "flower of Nipponese womanhood".
This trope is quite important in anime because housewives had its place in Japanese History especially during the neo-Confucian Japan. From tvtropes.org1:
The term was generally ascribed to noble women with traditional upbringings, but after the formal abolishment of the caste system it passed into wider use among the new "middle classes". Being a yamato nadeshiko revolved around the Confucian concepts of Feudal Loyalty and Filial Piety, which in the latest wave of Confucian revival meant acting for the benefit of one's family and obeying and assisting authority figures (father, husband, sometimes father-in-law or older brothers, as well as older and/or more respected females). Virtues include loyalty, domestic ability, wisdom, maturity, and humility.
These virtues stayed among Japanese women for generations and thus they are portrayed in anime medium as a way to show that Japanese women are very keen to get married and take care of her loved ones and be a housewife.
Gender inequality has been a huge problem in Asian countries typically in China and Japan. At work, it is reported that women are the last to be hired and the first to be fired. Many college-educated women simply aren't hired, even if they're qualified. There is still an expectation that a married woman will quit her job to stay at home. Sexual harassment, though technically illegal, is apparently common at the workplace and women had to quit because of that.
Moreover, the conflict between marriage and career is also one of the salient problems. In 2005, 59 % of Japanese women in their late 20s and 20 % of Japanese women in their 30s were not married. So, staying single for Japanese women is still seen as nontraditional or abnormal. Most of them are combined with negative meanings, such as urenokori (“left unsold”, refers to older than 25 year-old single Japanese women like the Christmas cake after 25th December, no one wants it), parasaito singuru (parasite single, describe adult children live with parents like dependents), and makeinu (“loser dog”, as opposed to a “winner” who is a married mother). Traditional ie or the ie system is the most prominent concept concerning Japanese families, which determines that women were valued and accorded status only as it related to their role as mothers. Although the ie concept was formally abolished in 1947, the core value of gender stereotypes still persists in every stage of Japanese society.
Both historical and modern viewpoints played a role in the portrayal of females in anime and manga. The adherence of above said "yamato nadeshiko" is more prevelant in shonen manga. In shoujo manga, the raw emotions of females are depicted with issues like long-distance relationships (where the woman work in a company and can hardly maintain her love life), love-triangles etc:
Most women in anime are either students, nobles, or an overworked corporate employee.
Probably the near complete abscensce of housewifes in western media makes you over estimate the amount that appear in non western media. That or you are reading a narrow set of genres.
