I think competition amongst today's students is already high. Students go through a lot trying to compete with other students to get into university, as well as to get into grad schools, and to compete to get the highest grades and best internships. I do not think it needs to be increased.
Schools are focusing too much already on competition among students. It is putting students who are not particularly school-skilled at a disadvantage, and discouraging them from trying harder because they know that they cannot compete. It would make much more sense for the focus of school to be shifted onto the personal growth of individual students, and the progress of individual students, rather than on constant comparisons.