First of all, there is a mention of the judgment of Paris in the Iliad – although it may not be where one would expect to find it. It comes in Book 24, and it is in fact included by H & P in their selections from the poem (H & P, pp. 438-439, lines 12-22).
One could also argue that the "Promethean prophecy" and "the failed attempt of Thetis to immortalize her son" are, in some form or other, crucial in understanding the Iliad. The importance for the Iliad of the myths centering around Thetis is developed by Laura Slatkin in her Power of Thetis (Berkeley, 1992). An excellent review of Slatkin's book by Andrew Sprague Becker is available online.