"j" is already used to represent another consonant that arguably sounds closer to Jay (not that it's supposed to specifically match how English uses the Latin a

"j" is already used to represent another consonant that arguably sounds closer to Jay (not that it's supposed to specifically match how English uses the Latin alphabet, but in this case it doesn't matter). Both of these consonants could maybe have been represented by "j" since they're always used in different contexts (IIRC), but pinyin avoids writing multiple sounds in the same way.