It doesn’t really matter if the scholarship is paid to the school or to the student. Schools require the student who is getting FA to report outside scholarships to the FA office and adjustments are made to the package. Many schools do allow the outside scholarships to offset loans, work study, or student contribution.
The original question is who benefits? Almost all students do. There are very few who don’t and those are the students who are already getting COA covered by grants or scholarships or full ride athletes like basketball or football players.