Was listening to I, Carrion again today and heard the things I've seen people talking about with icarus and the word Carrion (which might i add bird connotation in the song then brings in the idea of scavenger birds like Carrion feeders) but I realized something else also. Not sure if someone has said it yet but the way that Hozier sings "I, Carrion icarian" also sounds like "i carry on" as if even though fallen he has strength to still continue on or some other meaningful message through the song.
Another interpretation is the play of Carrion (decaying fleshed a dead animal/ death) so that it's literally I, Carrion Icarian, "I, dead and decaying icarus." Or even with my thoughts of wordplay, "I, dead and decaying, I carry on (Icarus)." Icarus was foolish but determined, so of course he would be known for despite the danger, carrying on into flying higher and higher to the sun.
Anyway, just my two cents.