The simple reason is that the use of Chinese characters in Vietnam, either with chữ hán or chữ nôm, was rendered progressively irrelevant in the early 20th century, and the new generations of literate Vietnamese used exclusively quốc ngữ to express themselves from the 1920s onward.

Chữ hán was an official language. It was basically literary Chinese used only for official communications and ceremonial usage. Its only (but important!) use beyond that is that it allowed its readers access to Chinese literature.

Chữ nôm was Chinese script used to transcribe Vietnamese words. It was used mostly for literary purposes - such as Nguyễn Du's Tale of Kiều, of course. But it was never taken up as an official language (except for a brief time during the Tây Sơn dynasty of 1788–1802), and was usually frowned upon by many literati who considered it as uncivilized (compared to the Chinese language) and mostly recreational, mirroring the difficult relation between Latin and vernacular French. One problem with chữ nôm was that it was unwieldy: unlike the Japanase kana, chữ nôm was not a systematic syllabary but consisted of an extensive set of more than 37,000 characters (Denecke, 2017).

Quốc ngữ has been invented by Portuguese missionaries in the early 17th century but remained used for at least two centuries only in the chrétientés, the Catholic communities. It was largely ignored by most Vietnamese, until a quốc ngữ press started appearing in the 1860s.

The latest addition to the mix was the French language, whose use was limited to the small numbers of people in direct interaction with the French: interpreters, traders, soldiers, staff etc.

By the late 19th century, none of these scripts was "winning". Colonial authorities, their Vietnamese collaborators, and Vietnamese opponents to French rule, all disagreed about the way forward when it came to a national writing language. Marr (1981) has described nothing less than 8 writing options for the Vietnamese at the turn of the century. The French and their collaborators were particularly divided between those who wanted to teach French to all Vietnamese, those who wanted to keep the Chinese characters, and those who wanted to spread the romanized script. Opponents were usually favourable to Chinese characters, and for a while chữ nôm was the favourite vehicle of opposition to French rule. And of course some literati were opposed to quốc ngữ, that foreign (well, non-Chinese...) script favoured by Catholics (a complete discussion of these extremely complicated debates can be found in DeFrancis, 1977 and Marr, 1981). How literate was the (largely rural) Vietnamese population remains elusive, but it is likely that part of the population - Marr estimates it at 25% of adults, but there may have been a large imbalance between genders - could read a few hundreds Chinese characters, not enough to read literature, but enough to read contracts, family records, and participate in ceremonies.

For most of the colonial period, the French were torn between their need to educate the Vietnamese so that they could be efficient subalterns, and their fear for the dangers of education, which could lead to the creation of dangerous déclassés and to the dissemination of wrong ideas. By the early 1900s, reformist Vietnamese were seeing quốc ngữ not as a despicable foreign import (like the previous generation did), but as tool for modernisation, notably due to its ease of learning: quốc ngữ, for all its faults, is simple and logical, and does not require learning thousands of characters, many Vietnamese-only. The nationalist Phan Bội Châu, who wrote in literary Chinese, called for the introduction of quốc ngữ into the education system (and his works were translated in quốc ngữ). Tran Tan Binh, a trusted collaborator who had been sent for year in France, came back to give lectures in Vietnam (cited by DeFrancis, 1971):

Let us study what is useful. Let us learn what the French, our teachers, have learned. We have a language which, thanks to Quoc Ngu, can be easily transcribed and learned in a very short time... It is a stroke of luck that we are endowed with it. In the whole world there is no country that can be called civilized which does not have its own language and writing. Language is an instrument; even more, it is like your hand, which serves for everything you do. To use the French language or Chinese characters for studying is to abandon the use of one's own hand, is to work with borrowed instruments that one first has to learn to use. Quoc Ngu is not hard to learn; three to five months will suffice for you to learn to read and write it fluently. Books written in Quoc Ngu will have the advantage of being understood by women and by children, by everyone. It is the only means of enlightening the masses of the people.

But the French were also wary of the association of quốc ngữ with ideas of independance (it meant national language after all). The Tonkin Free School (Đông Kinh Nghĩa Thục), which promoted quốc ngữ, was closed after a few months in 1908, and French authorities cracked down on the circulation of printed matter. But the Chinese characters were found to be potentially dangerous too: in the 1910s, the French cancelled the civil examinations, which had for centuries produced scholars and civil servants fluent in chữ hán, and had been the "primary mechanism that affiliated the ruling elites with the Confucian sino-vietnamese universe" (Brocheux and Emery, 2004).

By the 1920s, however, French authorities came to the conclusion that quốc ngữ was the safest way forward (they could not make millions of Vietnamese learn and write French, for some reason), and, while maintaining a tight grip on censorship, they made quốc ngữ the de facto written language in education and publishing, and sponsored writers who published in quốc ngữ, such as the monarchist Phạm Quỳnh (Nam Phong magazine) and Nguyễn Văn Vĩnh. As a result, the use of quốc ngữ literally exploded in the 1920s, with a mass publication of newspapers, magazines, poetry, novels, essays etc., ushering a true golden age of Vietnamese literary creation, with writers adapting the language to new forms and styles of literature. The first novel in quốc ngữ was published in 1925: twenty years later, there were about 400-500 novels available. This development was accompanied by private efforts at disseminating quốc ngữ in the population. These efforts were supported across the political spectrum: in 1938, the Association for the Dissemination of Quoc Ngu Study (Hội truyền bá quốc ngữ) was headed by conservative scholar Nguyễn Văn Tố (a nationalist but one acceptable to the French) and its assistant treasurer was Võ Nguyên Giáp (who had already a long career in activism). The "Soviet" movements of Nghệ An and Hà Tĩnh in 1930-1931 had made a point of organizing quốc ngữ classes.

Quốc ngữ writing had basically created its own momentum that appealed both to pro-French intellectuals and to the new generation of anticolonial nationalists, who found it a perfect tool for disseminating their ideas (many CP leaders had taught or learned quốc ngữ in jail!). In 1946, Hồ Chí Minh made the use and dissemination of quốc ngữ a national priority (cited by DeFrancis, 1971).

The government has decided that within a year from now all Vietnamese should know Quoc Ngu, our romanized national writing [...] Above all, it is necessary that everyone knows how to read and write Quoc Ngu.

In a nutshell, there was no turning back after the 1920s, once that quốc ngữ had been established as the national writing system, both by the colonizers and by their opponents. Chữ nôm did survive for a while (Denecke notes that vernacular verse narratives in chữ nôm woodblock print still had a readership until the 1930s) but it was irrelevant as an everyday written language. The next step would be the adaptation of the Vietnamese language (not just the writing system) to modern terminologies, but that's another story.

Sources

• Brocheux, Pierre, and Daniel Hémery. Indochine, La Colonisation Ambiguë, 1858-1954. Paris: Editions La Découverte, 2004.
• DeFrancis, John. Colonialism and Language Policy in Viet Nam. Contributions to the Sociology of Language ; 19. The Hague: Mouton, 1977.
• Denecke, Wiebke. “Shared Literary Heritage in the East Asian Sinographic Sphere.” In The Oxford Handbook of Classical Chinese Literature, 510–32. Oxford University Press, 2017. https://doi.org/10.1093/oxfordhb/9780199356591.001.0001.
• Marr, David G. Vietnamese Tradition on Trial, 1920-1945. Berkeley & Los Angeles: University of California Press, 1981.
• McHale, Shawn Frederick. Print and Power: Confuscianism, Communism, and Buddhism in the Making of Modern Vietnam. University of Hawaii Press, 2004.