American universities are in demand among foreigners because they are a gateway to network and life in the US.

If it's a choice between say Princeton in the US and Harvard outside the US, Princeton will be the choice for many.

Foreign students interested in a US education have diverse motivations and Universities in/of other countries have done well selling programs that compete with the US' institutions for students that don't have that motivation. Soon that may also be almost all of them.

not only, they're seen as the top institutions and even if you don't plan to stay in the us having a harvard or mit degree is enticing by itself.