The language/country norm is kinda irrelevant. In Japan John Lennon is not referred to as ”Lennon John”, nor is Miyamoto Musashi referred as "Musashi Miyamoto" in English.
For famous names, outside of official dpcuments people will use whatever names feels right to them and I personally think that should be fine as long as the name is recognized.
Not only that, we might be exposed to them for years without really knowing which is the family name and which is the given name!
In a vacuum, I might have guess "Chow Yun-fat" as starting with the family name because I know that the hyphenated, two-part names are usually given. But a name like "Yao Ming" I might not have had any idea, since I don't have the cultural exposure to know which single syllable words look more like family names versus given names.
Imagine expecting a Chinese person to figure out "Larry David" with no other context.
I believe that's a historical (19th-century) reason. Japan tried to live up to Western standards. They underwent radical changes and adopted Western culture, driven by the significant influence of the '脱亜入欧' (Leave Asia, Join the West) theory during the Meiji era. That's why they adopted a Western-style naming convention for English names (Personal name + Family name).
However, China and Korea didn't modernize as fast as Japan. They didn't have radical changes in the 19th century. (The result is that foreign concession in China, unequal treaties, colonization of Korea, etc.) So they didn't have to change their naming convention.
The reason why Japan is trying to change the English naming convention when they write in Japanese is similar to the reason mentioned above. The 21st century is Asia's century. Japan feels that they don't have to conform to Western standards anymore. They are trying to be more Asian. That's why they are attempting to change the convention to synchronize as if they were writing in Japanese.
For famous names, outside of official dpcuments people will use whatever names feels right to them and I personally think that should be fine as long as the name is recognized.