Yes, universities should compete for the best students regardless of nationality or residence, because it will encourage the smartest people from other nations to come to the United States. If these students stay in the United States, they can contribute to our economy by making new products which we can sell to other nations and improve the GDP.
Although I understand the desire for the need for affirmative action proposals, it hasn't changed the real elephant in the room - that the best universities are populated primarily by the financially privileged. I question the need for most universities to even question students on their nationality or residence, even the question of whether they are in-state or not. The only matter should be grades and qualifications.
If all the student would go to the UK for example, other countries will lose their best candidates. Yes, the UK will have an excellent group of student, but other countries' economic and financial markets will go down. There is also other factors concerning national security. Another thing - it is the government's duty to ensure that their own citizens get in, and if Uni's wouldn't accept a student of their own country, it can also lead to job shortage.