There was no centralised canon of "approved" myths. The ancient myths that appear in surviving sources aren't a matter of approving some and repressing others: it's more a matter of luck. Only a select few stories were lucky enough to make it into poems, and only a select few poems were lucky enough to survive.

Homer and Hesiod, in particular, weren't encyclopaedias, and they weren't contractually obligated to include every myth in their poems. The Iliad covers a few weeks of the Trojan War: it's not a place where you'd expect stories about Herakles or Theseus or Bellerophon (though figures like these do get mentioned in passing). The Hesiodic Theogony and Works and Days aren't places where you expect to find stories about heroes, wars, or aristocratic genealogies.

We do have a goodly amount of evidence for myths that we know were floating around in the 7th century BCE. We know some of these existed in poem form (Herakles, the Theban wars), but the poems haven't survived. In other cases there's no evidence for poems, but there's evidence from later periods or from the visual arts (the Argonauts, the Gigantomachy). There's literally no reason to expect them to appear in the Iliad or the Theogony, because that isn't what the Iliad and the Theogony were about.

So, the material we have is very limited. That's one thing to understand as a background to this question.

Another important thing to understand is the difference between local and pan-Hellenic legends and myths. There was a vast landscape of local legends, many tied to specific cities or regions. Many of them had no meaning beyond those regions. So there's no reason to expect the Iliad to include stories about how ancestral heroes in Pylos or Aitolia founded their dynasties, or about why Hades was popular in Elis.

Only a small selection of stories hit the big time. The biggest ones are stories that try to tie together characters from lots of regions: that's one reason for the success of the Iliad, because it explicitly sets about bringing together heroes from many, many parts of the Greek world. The Odyssey is a slightly different situation: Odysseus is from a small island, but his journeys acted as paradigm for colonisation and exploration. The Argonauts story did both -- gathering heroes from all over the place, and including journeys and exploration -- so it too had a pan-Hellenic status, but its medium wasn't primarily poetic, for whatever reason (until Apollonios came along and wrote a major poem about it: but that was centuries after the period we're talking about).

TL;DR: Don't think in terms of "omitting". The material that survives is only a tiny slice of what once existed. And survival is skewed towards stories that stories that stretched across multiple groups and regions, and only a very few stories did that.