What are some reasons why Odysseus should not be immortalized?

Odysseus is an important literary figure and thus it makes sense that students should continue to read the Homeric epics and learn about him. However, there is a difference between studying someone and idolizing or emulating that person.
Odysseus is a trickster figure such as Loki in Norse mythology or Coyote in the Native American tradition. What this means is that he is clever, but often unscrupulous. Two of his major exploits, the Trojan Horse and his defeat of the Cyclops, revolve around deception. A particularly morally questionable act is the deception he uses to try to obtain the bow of Philoctetes, as seen in Sophocles's play.
In Homer, Nestor combines wisdom with a strong moral compass as opposed to Odysseus who is clever but often seems more self-serving. While Odysseus's cleverness is essential to the defeat of Troy, and often tactically superior to more straightforward stratagems, the fact that he lies without remorse and is willing to use shady means to achieve his ends makes him a less than an ideal character to emulate.