Most non-native students of Japanese will almost always encounter that word in hiragana, katakana, or even Romaji--encountering that as a kanji is actually remarkably rare.
The fact that the kanji for kawaii is an ateji makes it one of those odd ducks.
Interestingly, it's very common for students of Chinese. The word 可爱 (kě'ài, "cute") is dirt-common, but it isn't native to Chinese -- it originates as a loan from Japanese.
This isn't clear to the Chinese themselves, who use 卡哇伊 (kǎwāyī) if they want to refer to the Japanese word.
There's another modern word for cute, 萌 méng, which is also a loan from Japanese, though I think popular awareness of it as a weird loanword is higher, since its literal meaning ("sprout") is so far removed from the concept "cute".
Have you ever been around non-native students of Japanese? This is the one word that is pretty much guaranteed to be known by all with an interest in anything remotely Japanese.
Your point is valid, but kawaii is perhaps not the right example.