Do US students have similar opportunities to study at foreign universities as foreign students have to study at US universities?

When comparing universities with similar entrance requirements (e.g. state schools, prestigious private schools, ivy league, etc.) are there a comparable number of US and foreign openings?

How often is instruction in English? (I realize this isn't entirely fair, but the reality is that high quality foreign language training isn't available at many US schools in the same way it is in Europe; which isn't the student's fault).

It seems to me that if the opportunities are not symmetrical then it is reasonable for there to be at least some protection/preference for domestic students. However, I think that needs to be balanced against the benefits of attracting foreign talent and expanding diversity. Either way, my understanding is that the US visa system is largely irrational and broken so it should definitely be reformed.