It says the origin of Hiragana is little later of Katakana. Hiragana was developed from character written in running style. It was used for unofficial documents such as poem, letter, etc between women of Kyoto. After that it became popular even for men as its simplicity and ease. Hiragana is different from Katakana which is aimed for writing with brush. It uses for Shodo (calligraphy), too.

There is no other culture uses two phonogram which has same purpose. How does it happen? Why those were not integrating into one? There is no answer for this question in this moment. We should wait until scholars reach to an conclusion.

Incidentally, Japanese ancient letters (before Kanji, Katakana, Hiragana) had phonetic and ideographic characteristic at the same time.