The fundamental story structures are quite similar. The scope of the tales told is quite similar. The behaviour of the protagonists and antagonists is quite similar.
We know about the Iliad and the Odyssey because they were relatively well preserved. We don’t know about Homer’s less popular poems, or of any particularly trashy verse that he wrote…because it didn’t survive.
The Iliad survived not because it is transcendent, but because it was popular (which meant that there were more copies made to survive over time). The "transcendence" was added later as a (probably wrong) reason for its popularity.
Some 3,000 years from now there will probably be someone calling the Saga of the Boy Wizard transcendent just the way that people call the Iliad transcendent. They, like many others, will confuse its widespread popularity and many copies with a judgement on quality. There are other similar stories better written that don’t have the popularity of HP. But they won’t survive over time because there weren’t as many copies.
I actually have no information as to the popularity of Homer's work relative to other works at that time. I suppose I have fairly strong intuitions as to its popularity after antiquity, but its popularity at that point seems to cut against your argument somewhat. There were certainly stories that dominated Homer's societal saturation after the fall of the Greek empire, and some of those survived, some not.