There are a number of fields where it is constantly claimed that we have too few graduates of, namely primary care physicians, engineers, and scientists. There is also a number of very good criticisms of our government that we are underinvesting in a number of basic research fields, energy especially but also materials science and a few other fields.
To create incentives to fix this problem a national research university system could be instituted. To encourage a focus on these majors, especially among people who fear they might not otherwise be able to afford college, degrees at this university would be free, with a contingency that a graduate work in the US for several years (5 being an easy number); similar to how we have service requirements for ROTC programs. Degrees would be limited to fields that we have a demonstrated need for, so available majors would be confined to the sciences, engineering, and medicine (though only primary care would be offered through this school with a requirement that graduates work in primary care for 5 years). Other courses would be offered in conjunction with the National Online University to provide a rounded education without requiring additional staff. All professors would also be funded researchers and, to the extent practical, students attending the university would be required to fulfill work study requirements that would involve acting as research assistants.
The narrow focus of these universities would limit competition with more traditional universities and the focus on research would help to fulfill another needed policy goal. Providing these degrees at no cost to the student would also provide valuable downward pressure on degree costs that existing federal programs such as loans and grants do not.