Nobody is illegally entering the country and then beginning graduate studies at Harvard, so if you understand this as an attack on universities and an attempt to essentially “close” the country then it makes perfect sense. That JD Vance interview where he went on about “we didn’t need immigrants to get to the moon” is probably the clearest statement of their outlook.
And the irony is that this would reject only those who properly did the paperwork and won't stop the people who prefer different methods of entry.