It seems that my statement about the Iliad being warmly embraced by Catholic tradition might not be as accurate as I thought. I've been reading up on the Iliad in the writings of the Early Church Fathers and they have some pretty negative things to say about it. The ones I've read so far (primarily St. Augustine and St. Justin Martyr) are arguing against the Theology of it to those who might still be swayed to the Roman religion, so the context is substantially different from that in which it would be studied today. Still it does make you think further about it.
I also came across a reference in a Sermon by Monsignor Ronald Knox on St. Ignatius Loyola regarding the dangers of Greek influences on the Jews at the time of the Maccabees. Here's the quote: "Gentile influences began to creep in - the Greek tolerance of false worship and of superstition, the Greek cult of beauty, the Greek contempt for morals."
So I'm still working to further understand the context in which we study the Iliad and the reasons for studying it.