[kijakusai]

Originally Posted by something

You can, but I guess the song lyrics (or whoever entered it into the HxH site) just didn't in this case. Some words (not sure how common it is with that specific one) are often spelled out in kana even though they have kanji equivalents.

It is OK to write yamato kotoba in hiragana.
There are people who tend to write yamato kotoba (Japanese words having their origins in the time before the introduction of Chinese characters) in hiragana or katakana. In fact, to write yamato kotoba excessively in kanji is often regarded as a thing that is done by undereducated people who try to feign to be well-educated (and by gaijin who have a smattering of Japanese and erroneously think sprinkling their Japanese writing with many kanji is a sign of being knowledgeable about Japanese). When Dr Keene Donald re-read Japanese writing which he had written in his younger days, he said those pieces of writings' having too many kanji suggested that he had been a 'newbie' who had tried to be cool.
So it is possible that when you read an article/book written by a Japanese man of letters, you see that yamato kotoba tend to be written in hiragana, rather than in kanji.
Yanagita Kunio criticised people who excessively applied kanji to yamato kotoba.

　最初自分たちでよい加減な宛字をこしらへて置きながら、それに引付けられて元の語の意味をその方へ曲げて 行くとは何といふ拙ないことであらう。ヤッカイといふ語は家と居との組合せで、本來はたゞ同居人といふこと であつた。是を公文に必ず厄介と書くことになつて、次第に此一語の感じを惡くした。兄や伯父たちと仲よく暮 して居る者が、この爲にどれ程肩身を狹くしたことか、考へて見ると宛字も折々は罪を作つて居る。以前是が非 でも漢字ばかりを以て男の文章を書かなければならなかつた時代でも、なほ今少し熟慮してもらひたかつたと思 ふことは多い。ましてこの自由な假名まじり文の世の中になつて、さういふ偏した立場から、文字に制約せられ ない人々を、嘲つたり戒めたりすることは、歷史を知つて居たらよもや出來ることで無からう。

Yanagita humorously called it the '(lower-middlebrows consult) cheap dictionaries (and excessively apply kanji to yamato kotoba and use too many kanji words)' evil.