Maybe the director didn't want the connection to be so much to Icarus but to the act of falling itself.
Nope. In an interview, director David Alden said:
"Icarus created his own wings but flew too close to the sun and plunged to his death. It's the ultimate image of someone seeking too much pleasure, life, and power, and it somehow accompanies the king throughout the landscape of his adventures and to his death. The king is a sort of Icarus figure."
Uh-oh, Icarus did not create his own wings; his father Daedalus made them for him. But just the idea of falling -- yes, that would have been good. Probably Icarus occurred to Alden simply because the story is so well known. Whom else could he have shown falling? Ozymandias? Would the audience know about those two trunkless legs of stone in the desert? I wouldn't count on it. It's a toughie.