It's a lament arising from the FALL FROM GRACE that is inevitably part of the human condition.
For me as a practicing Catholic, the poem has tremendous Christian-pagan tension. (angels; gods of stone and sound)
Deeply we long to live as pure spirit in this fallen material world but we get tempted and we get weak and we fall.
I wrote a play with an ex-monk in it. Why did he leave the monastery? For the pull of the world and the pull of the flesh.
Is the flesh inherently evil? Of course not. The uni-fleshness of the God-Christ has verily instituted a unitive sacred mystery (i.e. the marriage sacrament as a reflection of Christ's bond).
Note the poem has all sorts of gift and exchange references but none are of the blood or heart (the greatest sacrifice/gift we can make) or of nuptials (the form of the gift).
I think the Beatles lyric that responds well to this song is 'he-ey, you've got to hide your love away'. But only until after the vows of course.