I don’t think the large state-small state formula holds water. Pennsylvania is the 5th largest state in population, and Penn State’s undergraduate student body is 34% OOS, according to its latest CDS. Michigan is the 10th largest state by population and the University of Michigan’s undergrads are 41% OOS. Virginia is the 12th largest state and UVA’s undergrads are 28% OOS. Nor do these states have “bad secondary schools”; they’re all well above the national average in HS seniors’ ACT scores.
And far from “buying . . . top test scores,” many top public universities use OOS students as a cash cow, charging them higher OOS tuition while providing less FA to the OOS students. It’s a combination of academic quality and the campus culture that attracts large numbers of OOS applicants. It may not be “state” policy to “lure in outsiders,” but all the schools I mention operate with a high degree of autonomy from their respective states’ political branches, including setting their own admissions policies. They have multiple reasons to welcome OOS students, including shrinking legislative appropriations—in some cases now less than 5% of their operating budgets—as well as an interest in recruiting the academically strongest class and adding geographic diversity, both of which enhance the learning environment.