They have done.
The Japanese have Romaji which is the latin based script. It follows the alphabet a i u e o, ka ki ku ke ko and so on. This alphabet ordering is known as the gojūon. The hiragana ひらがな and katakana カタカナ (I have written in their respective scripts after the romaji) also follow the same alphabet ordering.
BTW Tōkyō is the correct Romaji or 東京 in Kanji.
Japanese tank designations in WWII incidentally follow the very old iroha alphabet i ro(go) ha ni ho order based on an ancient poem which contains all the syllables ( a bit like the English "quick sly fox....)
type 97 chi ha medium tank
97 九七 type 式 medium 中 tank 戦車 chi ha チハ
chi ha is the third tank in the series. 97 is the year the type was adopted ie last 2 digits of year 2597 which is from the birth of Japan in 660 AD hence about 1937. Simple when you know.
sayonara (romaji but should be accent on the "o" ie long vowel)
They are the most popular restaurants in Japan. In UK we have the Wagamama restaurant chain which is cultish and serves sushi, ramen noodles, and so on Japanese style. Teens and twenties( including my youngest daughter and her friends) would not be seen dead in a Macdonalds but love Wagamama. A culture topsy turvy.
BTW China also has a Roman script called Pinyin. It has been adopted throughout the world hence Peking is now known as Beijing and with the accents Běijīng.