Or to put it another way, how do you measure "equality of opportunity" if not by "equality of outcome"? If your theory of "equality of opportunity" differs from the measured "equality of outcome", doesn't that automatically mean you've omitted some characteristic of the real world from your theory?
Many aspects of our societies have lottery-like qualities.
But this seems like "too convenient" an explanation to me, it could be used to justify literally any system. For any system, one could assert that actually the opportunity is equal, but the variance is so great that the measured outcome "accidentally" arose out of the totally-equal-honest "opportunity" probability distribution.
I'm not prepared to accept such weak justifications of any supposed equal-opportunity system, I'd prefer to have a system where the outcome provided me with some verifiable indicator that the original opportunities were actually equal, in a similar sort of way where one can have verifiable proofs in cryptographic protocols.
That is indeed a large part of the point of the social/welfare state.