Could it make sense to get rid of scholarships?

Today I got the final bill for my daughter's fall semester. After scholarships and loans it is a relatively small (though still plenty large) amount of money.

It got me thinking, though, about what people actually pay for college. Especially in private institutions, few students pay the full sticker price. Instead each student pays some variant, with a big chunk of the tab being reduced by scholarships or other sorts of financial aid that students do not need to repay. Colleges monitor the amount of reduction (the "discount rate") very closely. The conventional wisdom is that a discount rate set too high reduces income for the college; one set too low discourages students from attending because it is too costly.

I wonder what would happen if instead of managing a discount rate, campuses just cut the tuition cost for all students by the discount rate and stopped giving out scholarships.

On the financial end it seems like ending scholarships would simplify the budget process. But I am more interested in what would happen to the make-up of the student body, and to their learning. Here are some surmises about the results of ending scholarships:
1. The campus would get fewer top academic students who normally take up nearly all of the full-ride scholarships.
2. In their place would come a more diverse range of students--more middling academic students, more students intrigued by the institution's offerings, and more first-generation students who would have been turned off by the high sticker price.
3. Students might end up paying less as a whole since they would not be subsidizing other students' attendance.
4. Aggregate retention, graduation, and other assessment numbers would decline modestly at first, since high achieving students are those most likely to be retained, graduate in 4 years, and be engaged in the life of the campus and they would make up a smaller proportion of the student body.
5. The campus would re-allocate resources away from programs serving high performing students (honors programs, targeted recruitment, etc) to the student body as a whole.
6. The re-allocation of resources and attention would eventually return agregate performance measures to previous levels.
7. Disaggregating these measures, though, would show improvement in the performance of students in "at-risk" groups.
8. The linkage between cost and quality would become clearer, since the cost to all students, the expenditures on all students, and the results of all students would become more clearly linked.
9. The campus would be forced to present itself and carry itself in different ways. It would no longer be so easy to trumpet its inputs (entering student GPA, SAT scores, fancy buildings, etc.) but it would be easier to focus on its mission and clearly describe cost to the public.

Are these 9 assumptions correct? Are there other likely outcomes? Is there anything that would make the risk of getting rid of scholarships worth the outcomes (which to me look positive over time)? Would it make sense at your campus?