You're right, fairness isn't at hand. But maybe we would tolerate being mean to some people and nicer to others as long as we're being fair—that is, we're efficiently matching worker to employer.
You say that one employer's neglect harms other employer's hiring. That's a good point, and it shows that organized applications, if applied across all firms, help everyone.
A single application system with a single deadline is kind of how universities admissions work. Maybe that's the best system we know. Can we have a system like universities admissions without the fees, is the real question?