How does word count work in Japanese ?

In English-speaking countries it is common for lecturers to place a limit on the number of words

My question is how does this work in Japanese, given that there's kanji and kana

If each kanji and each kana counts as a word, surely kanji is more dense (as in more message can be conveyed using fewer "words")

Doesn't this incentivize people to write more in kanji than in kana ? Is it common for essays to end up with much more kanji than normal writing ?