To know why there are Kun and On readings, you need to study the history of the Japnese writing system. Centuries ago, there was no writing system in Japan at all. Then the Chinese system was imported. So, at that time, if you wanted to write someting, you had to write it in Chinese. This went on for a long time.
Eventually, Japanese starting using Chinese characters to write Japanese words. (They still do.) This meant taking the Chinese character for "tree", for example, not using the Chinese pronunciation any more, and using the Japanese pronunciation (hence creating the Kun/On system).
However, in words that are combinations of kanji, the Chinese pronunciations were still used, even when writing in Japanese. It was important to keep track of which pronunciation of each character was being used. This persists onto this very day.
"...they have no purpose, and no one uses them..."? No way. Without the Kun and On pronunciations, the Japanese writing system would become useless.