They consider all those factors and then aim for a mix. No admissions board wants a class of 100% track stars or 100% economic hard-luck cases or 100% rich kids, etc. But they are faced with a bunch of kids who meet the GPA etc. criteria and also fit into each of these buckets.

Result is it's effectively random for each qualified kid.

That's all true, but you haven't described a lottery, you've described subjective criteria.