International students are mainly appreciated for the money they bring in. Many universities view international students as “cash cows” and even pay international recruiters who solicit full-paying applicants.
https://www.cnbc.com/2015/03/25/milking-the-foreign-student-cash-cow.html
https://consumerist.com/2015/10/01/colleges-paying-sketchy-agents-to-recruit-rich-foreign-students/
Smaller colleges who give financial aid seem to appreciate international students for their effects on admission rates. Advertise 10 financial aid packages/scholarships to international students, get 1000 additional applications from aid-seeking foreigners, lower your overall admission rate from 50% to 30%, climb in the rankings from #80 to #40.
Intangibles like diversity are nice, but at the end of the day, it’s mostly about money.