Since you accepted the premise when you said "if Omega shows up, I would...", then you must not be the sort of person who would pre-commit to an unpredictable coinflip, and you're just trying to signal cleverness by breaking the thought experiment on a bogus technicality.

Its not breaking the thought experiment on a "bogus technicality" its pointing out that the thought experiment is only coherent if we make some pretty significant assumptions about how people make decisions. The more noisy we believe human decision making is, the less perfect omega can be.

The paradox still raises the same point for decisions algorithms, but the coin flip underscores that the problem can be ill-defined for decisions algorithms that incorporate noisy inputs.