This argument is also used for Japanese, but I do not consider it valid.
This just proves that a phonetic writing is not sufficient, but it does not mean that the phonetic writing must be replaced with traditional writing.
To resolve the ambiguity of the phonetic writing, both in Chinese and in Japanese, where the ambiguity is much worse, it is enough to retain at most a couple hundred symbols to be used as semantic classifiers. It is likely that a great part of the traditional radicals would be suitable to be retained as classifiers, with perhaps a part of them omitted if redundant and a few other symbols added, if necessary.
Then the writing could be phonetic, but with classifier symbols attached to words, wherever the ambiguity makes them necessary.
This is not a new method. The oldest writing systems, like those of Egypt or Mesopotamia, also used classifier symbols (with meanings like: "a kind of human", "a kind of god", "a kind of animal", "a kind of stone", "a kind of wood", "a body part", "a kind of tool" and so on) attached to the words written phonetically, to avoid ambiguities.
If one would have to learn only 200 classifier symbols and with lower stroke counts than most symbols used now, that would be a great simplification.
Many of the Chinese characters are actually intended to be composed of two parts, a semantic classifier and a phonetic symbol, but this principle is applied too inconsistently and with too many variants, so the system can be greatly simplified by using a simple phonetic writing like Pinyin together with semantic classifiers inserted in the text only if they are necessary.