Quick answer: China does have a romanization system called pinyin for the Mandarin dialect which is quite accurate as long as you know the tones. Problems:

* Pinyin can't be used for other dialects, meaning someone in Guangzhou won't understand written pinyin.

* There are only something like 400 sounds in Mandarin, which means there are a lot of homonyms which makes pinyin not suitable in certain contexts.

* Switching a highly literate society with more than a billion people to a different writing system would be a massive undertaking.

The Vietnamese made such a switch from Chinese characters to a Romanization system based on Portuguese, but at a time when literacy in Chinese characters was relatively low and a colonial power (France) dominated the country and its bureaucracy.

I am not speaking about romanization, although it would surely be nice if all the cultures in the world used the same writing system. I am referring to what korea did with hangul.

Of course you address some of the pain points like the fact that China is way more literate than Korea was when Hangul was introduced.

Chinese is not a single language but spans a large subset of the Sino-Tibetan language family. They tend to mostly differ in their phonologies and not much in syntax and vocabulary, so written logograms could enable communication otherwise impossible. The script was also adopted by, for example, Koreans so they could do the non-verbal communication in written Chinese. You probably cannot expect this kind of uniformity across the whole Indo-European languages.

I don't know Chinese but I guess the text will become much more difficult to read. At least in Japanese there are many characters that have the same reading but different meaning. So with roman alphabet all those characters will be written the same way.

You mean apart from thousand years of history/records and billions of users?

I mean like Hangul

Hangul was possible because it explicitly targeted a single unified language (Korean was politically unified since circa 900 and the language was stuck).

And Hangul was also developed long time ago. And Korean(s) has way less users than Chinese.

Why should the number of users matter? The work factor per person is the same no matter how many people there are.

IMO, its because Han characters are a fundamental part of the national identity, and China has a fierce national pride.