No one uses “Latin” numbers, unless you count Roman numerals.
The numbers that we use in the west are often called Arabic numerals. They were actually developed in India so some call them Indian numerals.
People in the Far East adopted them for the same reason that people in the west adopted them: it’s a better number system than what they were using before.
For numbers, the same reason we use 1 and not one. 2468 is a lot easier to read than “two four six eight” or 二四六七, and they’re used the same in practice. Arabic numerals are universal globally.
For the letters, it’s just easier than trying to use Chinese characters. That one seems weird, but I guess pinyin is accepted enough that people know the characters and it makes sense.
Arabic numbers are generally understood universally around the world.
Western cultures had Arabic numbers introduced to them as well. The Ancient Greeks and Ancient Romans had their own number systems like Asian cultures. Fields like math, science and medicine made numbers and measurements more universal.
Elements of the language tend to follow technology or any other cultural trade or cultural phenomenon as it travels around the world.
Many places import Latin letters and Arabic numerals when they bring in technology developed from places which use Latin letters and Arabic numerals. You won’t find them in old ancient cultural texts, practices, etc. However, cars and license plates aren’t part of ancient Chinese or Korean culture. The license plates are one small part of vehicle technology which they imported. Numbers on a keypad, phone, computers, for most mathematics, all use Arabic numbers. Latin letters are peppered throughout general media and used in various ways (ex A, ex B, ex C, etc), but they are widely known for names of companies and organizations (google, Microsoft, IBM, Apple, UN, UNESCO, etc). These are not unknown elements to them, just like western scientists use a lot of foreign terms like Latin in classification systems, etc.
We can ask similar questions like why do we use Roman numerals in our movies, or latin abbreviations for things like pound.
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