You definitely don't need 大山-level mandarin to do business in china these days.
Plenty of foreigners work in China having much less than 6 months of Chinese. Most of them weren't even at my level. They still got by. Business meetings held with foreigners are usually in English anyways, it is only the old guard (Xi's generation) that can't English very well. And those people aren't so common in tech.
I don't think your numbers are right. Tibet has 4 million population. Xinjiang has 20 million, among which 50% are Han. Those are only 2 provinces where I can think of that doesn't require Mandarin to get by in certain area.
The rest of China, at least, could understand Mandarin without problems.
Guangdong province alone is 100 million people. Some of whom are Mandarin speakers (1st or 2nd or 2nd+ language). But many are not, not even as 2nd or 2nd+ language speakers. And their predominant language is Cantonese. Many people grew up before mandatory Mandarin education was instituted. There's a similar situation in other huge provinces all around China, especially southern China.