Then you don't have the "did we do enough for XYZ group", the RNG will simplify both decision making and justification. If there's x% of XYZ passing the minimum score, that's how many will be in your class.
The activists that are regularly called racist against asians proposed exactly this policy. It was called a "merit lottery" and worked by setting a GPA lower bound and then admitting students randomly if they had a GPA of at least that level. This policy was ultimately seen as "too extreme" and non implemented but it saw its fair share of "lefties hate asian success" and proponents were even called "enemies of excellence" by Scott Aaronson.
You can pour money into giving test prep help to disadvantaged groups and keep the headline, which is that fate decides among many who are worthy.