> Considering that there are over 300 million, yes million, people in China who do not speak Mandarin
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.