For younger generation this is not a problem, back in my college life where people in the same class came from different areas, from Xinjiang to Canton to the northeast corner. We have no problem understanding each other though sometimes funny with unique words or accents.
It seems that the problem is not as severe in China as in India.
It is similar to the way the Chinese government assigns non-native political officials to rule each region, and severely censors any politically controversial communication/media. That is, it is yet another tool of authoritarian social control, an effort to forestall any political opposition to the central government and its unresponsive top-down decision-making process.
India does not have the same kind of authoritarian governing institutions, so similar forced homogenization would not be politically viable.
Except they are not mutually unintelligible. Put someone from heilongjiang province in Sichuan and they will still be able to understand the language, albeit with more difficulty.
Though there are dialects that do have completely different pronunciation, they all use the same underlying script, save a select few minority languages. Mandarin Chinese is taught in school, but everyone still uses the local dialect to speak with each other.
I'm not even denying the CCP has ulterior motives in doing this, but your original claim was simply incorrect and disingenuous.
First of all, "Mandarin" is spoken not only in China mainland, but also the standard in Singapore and Taiwan. It was a creation by the Republic of China (which later became Taiwan government) back in 1923, long before the current Chinese government came into power.
Children use Mandarin in school because they have to learn it to be able to communicate with people coming from other parts of China, which would have become a huge disadvantage to themselves. (I can't imagine how I would communicate with other people in college otherwise) It doesn't mean people will forget how to speak their own dialect. In fact, people from the same region almost always speak their own dialects.
Regional / minority cultures are generally protected by the government. The minority are almost always over-represented in all kinds of national events. Being a minority in China means you can get tons of advantage (lower score required to enter good colleges, financial aid, etc.)
The statements "Bureaucratese is not mutually intelligible with Occitan" and "Mandarin is not mutually intelligible with Cantonese" are both true, but we could just say "French is not mutually intelligible with Occitan" and "Chinese in not mutually intelligible with Cantonese".
That's also not how standard French formed. Standardized French is Parisian French, so just the 'dialect' of the politically-important centre. Not too dissimilar to Latin (which was originally narrowly the dialect of Rome) in that.
Whatever the propaganda, China still contains a number of non-mutually intelligible (though related) languages, but of course Mandarin enjoys much prominence and has an enormous number of speakers.
