According to an answer on a related question:
In 1910, the physician oligopoly was started during the Republican administration of William Taft after the American Medical Association lobbied the states to strengthen the regulation of medical licensure and allow their state AMA offices to oversee the closure or merger of nearly half of medical schools and also the reduction of class sizes. The states have been subsidizing the education of the number of doctors recommended by the AMA.
There's likewise a shortage of spots in Germany and Canada. But are there any countries which have solved this problem and anyone passing the medical school entrance exam is guaranteed a spot at a medical school? In other words, I'm looking for countries where the number of medicine students is restricted by the number of talented people rather than a limit on how many students schools can accommodate.