The characters of 可愛い do not have the “correct” meaning. Just like in Chinese, 可 means “can”, or “possible”, and 可愛い is a weird exception. (It’s also nearly always written in hiragana.)

Nearly every word involving the kanji 可 in Japanese has something to do with permission: impossible (不可能), possible (可能), permission (許可), approval (可決), etc.

That said, the kanji-centric view of the world is ineffective, and one primarily adopted by beginner learners who have not spent any significant amount of time studying words in Japanese. It is always better to just learn words.

> the characters where chosen at least partly because of their actual meaning

Sure, didn't I say they were in my post?

The point was, in a discussion of how well X predicts Y, it's not very useful to examine a test case where Y came first and X was chosen post-hoc to match it.

> Sure, didn't I say they were in my post?

No, quite the opposite actually ;)

> the characters got arbitrarily attached to an existing word because they were similar in sound and meaning

It does not seem arbitrary in this case because the meaning does match.

I do take your point that using that word in the discussion above, which is about Japanese was not the best example. On the other hand, it is a good example in chinese.

(A) In Japanese the meanings don't match that closely. The word didn't originally mean cute, but rather pathetic or pitiable, and evolved over time. More info: http://gogen-allguide.com/ka/kawaii.html

(B) By arbitrary here I mean that there is no linguistic connection. "Arbitrarily chosen because they are similar" => "chosen for no reason other than their similarity".