Why would Auden only mention Icarus briefly in the second half of "Musée des Beaux Arts?"

The answer to this question is in Auden's words "for instance". His poem is not specifically about Icarus and his tragedy. It transcends this particular story, elevating its message to the highest, universal level. The poem is about suffering as an integral constituent of life. People are often completely unaware of other people's suffering. The Icarus motif is just an example, albeit a very drastic one. It serves as the poem's climax. The "delicate ship" is on its course and it keeps sailing, although the crew must have seen "a boy falling out of the sky". In other words, the strange death of a young boy changes nothing in the course of other people's lives. That is why, unlike Williams' poem, this one doesn't even have Icarus in its title, but the Museum. It deals with the relations of life vs. death and art vs. reality, rather than Icarus' tragic story.