Increasing matching efficiency reduces transaction costs. Those costs are huge, and they lower our quality of life and the dynamism of our economy.
Our financial markets are very liquid most of the time. An underappreciated fact is that the aforementioned liquidity increases investment and keeps America on top of the world. Our labor markets aren't nearly as liquid. That is why there is a disconnect between how well corporations are doing and how well employees are doing. Both people and corporations would be better off if our labor markets were more liquid. We currently don't have the tools to make that happen. However, they are easy to create. They just need widespread buy-in and agreement on the core problem of inefficient matching in the labor markets.
Think of all the people who would have benefited from internships they never got and better jobs that they never applied for. If they got those internships and got those jobs, not only would they benefit, the whole country would benefit. It is in our collective interest to 1. keep people employed 2. at the best job at the best company 3. that is equal in quality to the person's qualifications. You can bring up the fuzziness and subjectiveness of qualifications and job quality, but let's be real. We all know who from our graduating class can get a job at an SP500 company and who can get a job at a Russell 2000 company. Both would benefit from a common app-style job application for different reasons. Let's stop pretending otherwise, because that hinders innovation and keeps us in the unsatisfactory status quo.
I'm not so sold on the idea that a match system will improve labor liquidity. How do you negotiate wages? Medical residents are stuck with the salary of the site that they matched at. When you enter the match, you cannot simply choose not to accept the job "offer" you are given.