I think the assumption is that <PERSON>'s songs are an expression of something more complicated than power.
<PERSON> has this to say on <PERSON> in letter 144:
<PERSON> is not an important person – to the narrative. I suppose he has some importance as a ‘comment’. I mean, I do not really write like that: he is just an invention, and he represents something that I feel important, though I would not be prepared to analyze the feeling precisely. I would not, however, have left him in, if he did not have some kind of function. I might put it this way. The story is cast in terms of a good side, and a bad side, beauty against ruthless ugliness, tyranny against kingship, moderated freedom with consent against compulsion that has long lost any object save mere power, and so on; but both sides in some degree, conservative or destructive, want a measure of control. 417
But if you have, as it were taken ‘a vow of poverty’, renounced control, and take your delight in things for themselves without reference to yourself, watching, observing, and to some extent knowing, then the question of the rights and wrongs of power and control might become utterly meaningless to you, and the means of power quite valueless. It is a natural pacifist view, which arises in the mind when there is a war.
As an embodiment of a pacifist position, he can't be said to have "power" at all, and neither can his songs.
Political power, martial power, magical power, the power of the rings, are all inherently "corrupt" in that their aim is to alter the tide of affairs, to change the world as <PERSON> made it, in order to serve the aims of those who wield power (even if they intend to do something good with it). The ring, as the physical manifestation of the will to power, represents this inherent corruption.
<PERSON>'s songs, like those of <PERSON>, are linked to the creation of the world, to the perfect condition of things before they are corrupted by greed, or pride, or the other failings of beings. <PERSON>'s "power" if he has it, is to be of a world untouched by these failings and not to want to exercise power at all, but rather to be imbued with what remains of a world untouched by it. <PERSON> is so untouched by power, so immune to its influence, that even the ring has no effect on him. His essential essence is effective in Middle Earth (against corrupt wights and tree spirits, etc.) because it is part of the perfect state of the world close to its creation, something that is, in itself, effective. This state is something shared by his land, and his songs are essentially conservative - they reassert the original condition of the world by repeating the process by which <PERSON> created it. 72