It doesn't work due to the insane amount of homophones. When you are speaking with someone you have context and you can discern the meaning of what it's said. But random words or texts can change it's meaning depending of what character is used. And the tone system doesn't help as it can be seen in Chinese pinyin.
For example, how many kanji can be read as 'shuu'/しゅう: http://jisho.org/search/%E3%81%97%E3%82%85%E3%81%86%20%23kan...
Try to do that with tones.