Why do people in Chinese mainland and Taiwan Province Province speak so much Mandarin?

Because all those Putonghua were brought by Chiang Kai-shek, he came here with his subordinates after the setback of the liberation war. His subordinates were basically from the northern region, so they all spoke Putonghua, which is what they called "standard Putonghua", so it was basically the same as the mainland Putonghua.

But when you think about it, it's still not quite the same as the standard Mandarin in Chinese mainland, mainly because of immigration, and a lot of similar Shanghainese, Jiangsu and Zhejiang dialects, plus some local dialects and Minnan dialects in Taiwan Province Province, which naturally seems a bit strange.

However, personally, many standard Putonghua pronunciations in Taiwan Province Province adhere to the ancient Chinese pronunciation, which is a relatively correct pronunciation.