Maybe you were expecting "Siren Song" to sound more like, well, a song. That seems reasonable enough. But the fact that we never hear a real "song" per se is what makes this poem, and the purpose behind it, all the more relevant to what a Siren really is. A song can't be mysterious and alluring if we can anticipate exactly how it will sound and what it will do. So this "song" that doesn't really sound like a song is exactly the sort of thing a Siren might sing in order to catch us off guard and therefore keep us ripe for seduction.
Our "song" sounds more like a conversation that the speaker is having with us. Unfortunately we don't realize just how dangerous the song really is until it's too late. That's because the lines nevertheless flow effortlessly into one another, as they would in a conversation. That smooth-sounding flow is no accident, though. It's achieved through enjambment and idiomatic language. Together, these techniques combine to make the poem sound informal and casual (as in, "get me out of this bird suit").
But there are also times when we're reminded that we're still dealing with a poem. The anaphora we see in the repetition of phrases like "the song" and "only you" helps to maintain the song's poetic sonic structure without sounding too artsy. Repeating those key phrases also serves the purpose of hypnotizing us with all the flattering and alluring language that encourages us to "come closer," as we're lulled into a daze of feeling special and unique. So, even if this isn't your typical "song," it still has those poetic qualities that make for an enchanting sound that "works every time."