Here is an article calling for a match. The opening paragraphs describe the current, unraveled recruiting process.
The Case for an Epilepsy and Clinical Neurophysiology Match
Pediatric Neurology, 2017-07-01, Volume 72, Pages 5-6, Copyright © 2017 Elsevier Inc.
"Accredited epilepsy and clinical neurophysiology fellowships in the United States do not participate in a formal matching system to facilitate selection of trainees. For the 2015 to 2016 academic year, there were about 95 accredited clinical neurophysiology fellowship programs offering 313 positions and 43 epilepsy fellowship programs with 106 available positions. Each of these programs has their own unique recruitment process. The lack of a standardized process may be disadvantageous for both applicants and the training programs.
With our current approach, applicants may feel compelled to accept a fellowship offer before completing other program visits and with little time to consider their options. This situation occurs when a position is offered on the spot or soon after an interview. Unless the offer is quickly accepted, the candidate risks losing a guaranteed opportunity in order to explore other programs. The lack of uniformity in the application process can create additional difficulties for applicants.
Similarly, knowing that good candidates are likely to receive offers from other institutions during an interview, many institutions feel compelled to make a quick decision in their selection of fellows. In an effort to avoid vacancies, program directors may be tempted to select applicants who are available but may not be the best choice. Adopting a formal match system would create a more organized process with clear advantages for both applicants and programs."