I think you have it backwards: targeting "equality of outcome" necessitates policies to pick winners and losers. Specifically, it requires policies that aim to minimize both.
Equality of opportunity doesn't mean hobbling talented people or enforcing that everyone be given identical opportunities. It simply means that people regardless of talent (in a given ability) ought not be restricted from an attempting to take an advantage of an opportunity should they happen to have it.
All admissions policies pick winners and losers, that’s the point. A collage which sifts the relative importance of SAT scores vs GPA is picking winners and losers, it’s hardly an argument in favor of any specific policy.
AA increases how much innate talent matters vs some peoples social position. It’s the same outcome as removing legacy admissions, just with a slightly different set of beneficiaries.
Collages have many leavers to get these kinds of outcomes. Favor elite prep schools and suddenly you have a surplus of high income families etc.
Equality of opportunity doesn't mean hobbling talented people or enforcing that everyone be given identical opportunities. It simply means that people regardless of talent (in a given ability) ought not be restricted from an attempting to take an advantage of an opportunity should they happen to have it.