Then employers would fight over the applicants that have this other feature, rather than those with the university education.

That is only true if the new signal partially screens off education. If the employers have the choice of using the joint signal, what matters is the additional value of the education signal beyond the new signal. If you found a signal completely unrelated to education, it would not reduce the value of the education signal. For example, if employers value IQ, diligence, and honesty, but only the first two contribute to education, then an honesty test would not reduce the value of education, while an IQ test would reduce the value of education to just the value of diligence.