For some reason I seem to remember that I *have* heard Ayu say "omae" in some video before.
Maybe it was some backstage thing or something...
Anyhow, most has already been said, but one more point I'd like to make is that sometimes I feel like Ayu's use of "boku" makes her lyrics more personal, like she's really trying to close the distance between her and her listeners. I mean, if you're talking to a close friend, you wouldn't really use words like "watashi" or "anata" at full force or anything. To make her lyrics more appealing to her fans who feel like they are closer to Ayu through her lyrics, or try to relate to her lyrics, it's actually quite good to use "boku" and "kimi". The use of these pronouns just seems to be warmer.
Also, I think we should look at pronouns in Japan less as a gender-specific thing and more as a hierachic thing. In modern Japan it's not really "I'm a girl I must use watashi" and "I'm a boy I must use ore" (since it's apparently very weird if a grown boy still uses 'boku'. I think it's considered something that a small boy would use. XD). It's more like "I'm talking to someone above me, must be formal." That's why I don't think it's really much of a big deal that Ayu uses 'boku' at all.
From an artistic point of view, not only is this completely plausible but it also works in Ayu's favour because it makes it easier for the listener to relate to Ayu's lyrics too. In Japan's social context, it's not at all uncommon for girls to use 'boku', either. Language isn't that rigid.
