[Uemarasan]

Uh, you just said it yourself: "I do feel that Ayu's lyrics are deep, and show profound emotion." Why should there be a clear distinction between what comes from the heart and what comes from the brain? It takes a heightened awareness and intelligence to express deep and profound emotion in writing that, in the first place, makes sense (which most emo music fails to achieve). I think you're referring to cerebralism, and Ayu is not a cerebral lyricist. If you really want me to argue for the sake of Ayu's intelligence, this might take a while:

From "Marionette":

First of all, the song is about the consideration of our life experience:

Memories are always beautiful
In the eyes of everyone
In the same way
...

We can look back on the past
Because we passed there
We stopped and stepped forward again

Our tendency is to make sense of our life experience, to rearrange it in a way that is pleasing to us. We always transform our lives into some form of beautiful story (memory), and so Ayu compares this to staging a marionette play. The past has been romanticized and elevated (Memories are beautiful...), life has been transformed into a drama that we stage for our own reasons. But:

But, yes
We actually know
That there is more

...

We were not born to live
Just putting on a front
And hiding a face
Like the dead

She argues against trivializing life as such. We have unwittingly turned ourselves into the marionettes of our own play, our true selves sublimated into the facade of beautiful memories, beautiful stories. In a sense, it is a kind of death. A denial of life. She skillfully introduces a metaphor here: the idea of a death mask is equated with the face of a marionette, which is, in a sense, a mask in itself.

Now, let's stand up without fear
For the sake of no one else

And rip off the masks
With our own hands

A death mask is used as a presentable face and in fact serves to disguise the dead face beneath it. When we stage our lives carefully like a marionette play, we are depriving it of the messiness, even the ugliness, that life should possess. Life becomes carefully determined, and we manipulate ourselves like marionettes, animated by something resembling a life force but is really not. So she says: stand up without fear, deface our marionette selves, rip off the masks we make for ourselves, that render us dead, and present our true living faces for all to see.

That, I believe, is as close as it gets to poetry.