Med Students and residencies are pretty unique, however. You're technically still in school and can't just leave at the drop of a hat and still meet the requirements to graduate, which you need to do in order to accept the job.
Plus you would be forcing not only yourself to go to a bunch of interviews maybe even as early as February of your 3rd year, you would also be forced to commit on the spot to a particular offer if given the choice.
The match process allows for the time you need to go on interviews, for programs to get a feel for the types of applicants in the pool, and allows you to shop around for programs as well. It takes a whole lot of power out of the hands of the programs and gives it back to you
Yes, that's how it would work in a perfect market. This is not that. It is similar to a regulated monopoly, which is the best system we can come up with at this moment. Competitors, like I stated before, would mess up the process for a lot of years and we don't have the time right now, given the increasing cost of medical care and the impending shortage of physicians, to screw up a process that has worked for quite some time.
The websites you use everyday pay for it with advertising, donations, and subscriptions. I don't want my official process to be offering me "One weird trick to get into residency" in the sidebar. Donations wouldn't happen. And a one-time fee makes more sense.
This is a complex system of verifying applicant information and presenting it all in a way that maintains the integrity of your data and the process of offers. The algorithm in use won a Nobel prize and they have updated it to requests for couples matches and advanced matching. It requires a lot of people to maintain all the infrastructure surrounding the process and a tiny fee (you can apply up to 10 programs for a mere $95 and a transcript fee...hardly through the nose) is all you pay. That might seem like a lot of money, but it's due to the fact that disseminating the information is a lot more complex than just sending an email and hosting a letter.