That's because they aren't dialects. They are different languages. The CCP has pushed this lie that all Chinese languages are "dialects" instead of separate languages because it aligns with their narrative of a single Chinese people. You can be a single ethnicity and still have differences and different languages, but to the mainland government differences undermine cohesion.
The differences between these so called "dialects" are larger than between the Romance languages to each other. Thus, there is more mutual intelligibility between Spanish, Portuguese, and Italian than between Taiwanese, Mandarin, and Cantonese. To call them "dialects" is linguistically incorrect. They are separate languages. Someone will always respond that they are mutually intelligible through writing, and that's true. But that's bc the writing system isn't actually portraying the verbal language. It is a pictographic script.
> The Chinese (or 'Sinitic') languages are typically divided into seven major language groups, and their study is a distinct academic discipline. They differ as much from each other morphologically and phonetically as do English, German and Danish, but meanwhile share the same writing system (Hanzi) and are mutually intelligible in written form. There are in addition approximately 300 minority languages spoken by the remaining 8% of the population of China. The ones with greatest state support are Mongolian, Tibetan, Uyghur and Zhuang.
CCP did everything it could to wipe out old traditions, and replace them with communism and cult of leaders. Latter they realized it is not enough to keep coherent national identity, and started promoting a few symbols they liked from past. The "big red door decorations" is not Chinese culture, it is a small fragment of it.
> It is simply absurd to claim Chinese culture only survived in "a few small places" in the mainland.
I do not claim that. It did not survived at all on mainland. "A few small places" are outside of mainland: Taiwan, Honk Kong, Macau and perhaps Singapore.
So your claim is even more absurd. I guess that language they're speaking on the mainland must be French then?
Look what CCP did to languages (other than Mandarin), ethnic identity (other than Han) and writing systems.