Chinese writing is not phonetic, while a western alphabet would necessarily be phonetic.
One may think that is a disadvantage for Chinese, but since there such a wide variety of spoken Chinese languages, Chinese writing acts as a unifying framework across different spoken languages.
This allows a (more or less, ignoring traditional and simplified) common script for one billion people.
So a person in Taiwan can reasonably read a newspaper in Taiwan, Hong Kong, Shanghai, and Beijing. But that same person would probably have trouble speaking Cantonese with Hong Kongers.
There is a similar thing going on with written arabic, where Ḥarakāt diacritics indicate short vowels, long consonants, and some other vocalizations, but these are generally left out of writing except in the Qur'an. So you have a classic phonetic key with which to recite the Qur'an, but almost all written text besides that can be read by wildly different speakers.
I'm amazed at how two (Mainland) Chinese people can always communicate.
The level of shared cultural foundation is beyond what we have in Europe, I believe.
While they use the same script, they are not interchangable. A person from Taiwan would recognize characters in a HK or Japanese newspaper but would not necessarily understands it. A good half would only make sense to someone who speaks Cantonese.
Also, several languages have moved from a script if iconographic characters to phonetic ones: for example Vietnamese and Korean, the former adopting a phonetic western alphabet with accents, and the latter developing a new phonetic script, hangul. Japanese developed two new syllables based scripts, hiragana and katakana, which are mixed with the old word characters (kanji). All these used to use Chinese styles characters prior to the switch.
No reason Chinese couldn't do the same. In fact, it did… pinyin is a formal phonetic alphabet for Mandarin Chinese that's based on the western alphabet with additional marks denoting the tones of the words. It's only hard I'm an educational setting, but you could use it anywhere!
Someone from Taiwan can read a HK newspaper no problem.
The pinyin phonetic alphabet only works for mandarin, while a unified written script applies beyond mandarin.
Learning written Chinese not only connects you across varying spoken Chinese languages, but also connects you with the rich history of Classical Chinese text.
The formal pinyin system is great, and should be used along side with the actual Chinese characters. But there is no reason to replace the rich written Chinese characters, which connects across space and time, with a narrow and hollow substitute.
One may think that is a disadvantage for Chinese, but since there such a wide variety of spoken Chinese languages, Chinese writing acts as a unifying framework across different spoken languages.
This allows a (more or less, ignoring traditional and simplified) common script for one billion people.
So a person in Taiwan can reasonably read a newspaper in Taiwan, Hong Kong, Shanghai, and Beijing. But that same person would probably have trouble speaking Cantonese with Hong Kongers.