Why are Chinese place names and names translated into English in Pinyin instead of English grammar? Can foreigners understand it? Beijing should be Beijing, right?

Before the reform and opening up, China people's names and place names were spelled according to the Vedic alphabet. For example, Peking was spelled Peking, Nanjing was spelled Namking, and Deng Xiaoping was spelled Teng HsiaoPing. This spelling began in the Republic of China and has been in use for a long time. At that time, in English class, students should first make clear that their English name spelling is different from Chinese Pinyin, and also learn how to spell their own names in English. If you have an old dictionary or an old English textbook from the Cultural Revolution or even earlier, you should find many such spellings. Probably after the reform and opening-up, the Chinese names of English gradually changed to direct spelling of Chinese Pinyin, and I don't know when it became a national regulation. Only some pre-liberation words or individual names are still spelled in the old way, such as Peking University or Peking University, Peking Duck or Peking Duck. Only Taiwan Province Province, such as Taibei and Kaohsiung, still uses the Vedic alphabet. The usual joke is that the translator transliterates Chiang Kai-shek without knowing the changing history of China's translation. To tell the truth, this change has both advantages and disadvantages. The pronunciation rules of Chinese Pinyin and English words are not the same, and foreigners are no better than Wade's phonetic symbol standard, and the cost of revision in all walks of life is also very high (don't forget that it was an era without computers). Moreover, many languages other than English have different pronunciation rules from English, so the transliteration of Chinese names and place names must be handled separately.