Not enough information. For example, in English some of the least common characters are also generally not important for conveying information. Your argument o

Not enough information. For example, in English some of the least common characters are also generally not important for conveying information. Your argument only holds if Kanji was designed to be optimal in compressing information, which is of course not how Kanji came to be. That doesn't mean you are wrong, but your argument is invalid.