Why the Y Combinator instead of the Omega-combinator?

Likely an absence of an incentive to investigate alternatives along with the fact that an infinite number of fixed point combinators exist in addition to social capital/inertia. One of the two people who is regarded as originating combinators even though the K combinator is Peirce's Law (1885) and the S combinator is Hypothetical Syllogism published the first fixed point combinator as the Y combinator (Curry 1930) and by association has been promoted as "the" fixed point operator (example). Also, Ω is a Greek (Unicode) and not a standard Latin (ASCII) character. The X combinator is similar to Ω in that they are the shorter basis and fixed point definitions respectively at a cost of a small number of additional steps in some proof applications.