How could you argue that Agamemnon deserves Achilles' armor in The Iliad?

The story of what happens to Achilles' armor after his death is not actually told in the Iliad but appears in a lost epic called the "Little Iliad". Sophocles's Ajax is based on the dispute between Odysseus and Ajax over who should be awarded the armor. The two kings, Agamemnon and Menelaus, judge the dispute, but were never actually in the running for the armor, which was to be awarded to the greatest remaining warrior. Neither of the two kings were outstanding warriors.
Ajax is a warrior of the traditional heroic mold, physically strong and brave, proud, stubborn, and quick to anger. Odysseus, although lacking in Ajax's strength or heroic flair, is far cleverer and more effective. He is known for his cunning and his intelligence enables him to be more effective than the physically more impressive Ajax. Thus the kings with the collusion of Athena (the patron goddess of Odysseus) award the armor to Odysseus, at which point Ajax goes mad.
There would really be no point awarding the best available armor to Agamemnon who is not one of the stronger fighters in the army and does not really belong on the front lines.