There are many instances where this happens in Japanese. For whatever reason, sometimes the Kanji is not used with a word.
Here's a few examples:
有り難う (kanji form)
宜しくお願いします (kanji form)
今日は (kanji form)
Off the top of my head there are four reasons why this happens (possibly more).
- Kanji is sometimes omitted from specific words to avoid using too much kanji in text, as sometimes it can be intimidating to see too much kanji in a sentence.
- Sometimes kanji isn't used to make things easier for kids/laymen to read.
- Sometimes a conjugated form doesn't fully mean the same thing as the plain form.
- Sometimes the kanji isn't used because of tradition.
Of the cases listed above, in this circumstance, what you are seeing here is likely the result of case 3 (and possibly 4 as well). This kanji is usually taught to 4th grade elementary school kids, so it isn't hard for most Japanese people.
付く (usually written つく) has the meaning
to accompany; to attend; to follow (see definition 6). This particular meaning of つく is usually written without kanji to avoid confusion with 付く (which usually uses the kanji), meaning
to be attached; to be connected with; to adhere; to stick; to cling (see definition 1). While the two words do technically have the same kanji, the meaning of the kanji is just different enough from 'to follow' that it is left off in these circumstances.