Why we don't use the term "Omniverse" anymore except for joke characters:
No source seems to agree about what it is.
1) The Marvel handbook defines it as all of fiction and reality combined. If this is the definition, then no fictional character can logically reach this high, as each supposedly "omnipotent" fictional entity only has influence over its own fictional continuity. Their reach stops with the copyrights for the franchise, and they certainly have no influence over our reality outside of fiction.
2) Other definitions of omniverse include the one given in Mark Gruenwald's Quasar run, as an infinite collection of multiverses, in which case it seems to be a 6- or 12-dimensional structure. Given that Mark was likely the one who originally came up with the term "omniverse" in the first place, this is also certainly a very relevant definition.
(As an extra contradiction, the Marvel handbook has apparently also embraced this version of the definition on occasion.)
3) In addition, the Merriam-Webster dictionary defines an omniverse as a 7-dimensional universe (3 spatial and 4 temporal dimensions), Wiktionary defines it as a collection of universes, and Spore defines it as a 10-11-dimensional space.
Meaning: Alternative #1 means that an omniverse is too great a term to use to classify any character, whereas the other ones mean that it is far too small to define the greatest ones.