Should a country publicly fund higher education for its best and brightest? Of course. It might be direct funding or government sponsored long-term loans repaid from future earnings after an income threshold is reached, or even something else.
What about students from other countries or degrees such as MBA's? Probably not.
In the second case, university income from full fee paying students shouldn't be instead of other government funding as this can have other perverse effects such as forcing growth and degree's that do not help further the aims of higher education.