I'm a huge advocate of higher education, but it seems like a bad idea to fund it in a major way with the tuition of foreign students. Far better to provide those students education without a premium, or perhaps even at a slight discount.
Do you have any evidence of the zero-sum nature of your comment? That international students are taking spots away from local students?
UCF is a convenient example for me:
UCF is informally known as "U Can't Finish" because the classes fill up before all the students can register. You can see the complaints on /r/ucf around registration time, and I've heard about this personally from people who have experienced it. For example, a CS student can't graduate because the physics classes all have over 150 people waitlisted.
According to wikipedia, "enrollment today exceeds 66,000 students from 157 countries, all 50 states and Washington, D.C.". The school is 4% international and rejects 50% of applicants. Unless nearly all of the rejected students are international, there are many non-international students who lost spots to the international students.
It definitely isn't a zero sum gain for everyone. A lot of money comes into our economy in general from international students. And in a sane environment, we would try to keep them here when they graduate.
But pretending it isn't an important component of college price inflation in a country ruled by supply and demand, and the power of the almighty dollar, doesn't make sense either.