Some quick Googling surfaces the number of residency slots as being another limiting factor to medical school admissions. Apparently, federal funding caps the maximum number of residency slots which creates a bottleneck in the system.

It's most likely the case that there are multiple different bottlenecks. It's not just 1 person in a room somewhere saying "we need to make protect the elite!" - it's more likely just a lot of people continuing the status quo and few people fighting the change it.