I asked a history professor this when I was in undergrad and the only answer he had for me is that in the classical system, medicine was taught only after someone had gone through the trivium and quadrivium and the US system was just a continuation of that. However, if that was the reason, wouldn't it mean that the UK should also have medicine as a graduate degree instead of an undergrad one?
Not sure if you ever got an outside answer to this question, but the major difference between U.S. and Canadian medical schools and their European cousins hinges on the Flexner Report commissioned by the Carnegie Foundation that came out in 1910.
Before the report came out, medical education was a mess in the United States. In essence medical education ran the gambit from universities like Johns Hopkins that required a 4-year undergraduate degree to little rural groups of doctors that practiced medicine and taught on the side.
Any group of physicians could come together and form a medical school and the quality of education they provided varied wildly. They would accept any student who could afford to pay for their lectures. These little medical colleges often didn't require even a high school diploma, much less a college degree. They would sell tickets to lectures to support themselves. Students would collect their tickets into a booklet, and as soon as they collected the prerequisite number of tickets for that college they could call themselves "Doctor."
At this point the young physician would find a mentor and begin an apprenticeship under an established physician. This apprenticeship would last until the mentor physician deemed his/her mentee ready for solo practice and might even invite them on as a partner.
By the early 1900’s there were 155 medical schools across North America, and no central quality control of the education these schools provided. This meant that there were many underqualified physicians practicing “medicine,” some of whom were no better than snake oil salesmen. In response to this the nascent American Medical Association commissioned the Carnegie Foundation to study the state of medical education in the United States and Canada.
The Carnegie Foundation turned to Abraham Flexner, a Johns Hopkins University trained education reformer. To complete his task, Flexner went to each and every medical school in the U.S. and Canada, sat in on lectures and evaluated the quality of education at these schools. He based the medical education at Johns Hopkins School of Medicine as the gold standard in North American medical education. Johns Hopkins, in turn, had been founded by some of the most renowned medical minds at the time. Many of whom attended medical school in Germany which was the seat of outstanding medical education in the world during the middle to late 19th Century.
At the conclusion of his study, Flexner created a book length report recommending many changes to medical education and suggested that the number of medical schools in the U.S. and Canada be reduced from 155 to just 31! The report included scathing reviews of nearly every single medical school he visited. Some jewels of his reviews include:
Both the Arkansas schools are local institutions in a state that has at this date three times as many doctors as it needs; neither has a single redeeming feature. It is incredible that the state university should permit its name to shelter one of them.
The situation to be dealt with in this state [Georgia] is so simple that there is no room for difference of opinion as to what to be done. … The two eclectic schools, as utterly incapable of training doctors, should be summarily suppressed.
Of the four medical schools in the state [Iowa] none is at this time satisfactory. The osteopathic school at Des Moines is a disgrace to the state and should be suppressed.
Indeed, the Flexner report was so damning that the number of medical schools in the U.S. and Canada shrank from 160 in 1904 to 66 by 1935. Many of these schools closed outright, and some actually merged per the recommendations of the report.
In addition to his review of medical schools, Flexner laid the groundwork for modern medical education by mandating that all aspiring physicians hold a High School diploma, receive at minimum two years of prerequisite education at the university level, and set the structure of medical school to two years of pre-clinical education grounded in scientifically valid fields of study including Human Anatomy and Physiology, Biochemistry, Microbiology, Pharmacology, and Pathophysiology. Following the two years of pre-clinical education, students would then spend two years of clinical education rotating on the wards gaining experience in the major fields of medicine including Medicine, Surgery, Pediatrics, Obstetrics and Gynecology, and Psychiatry.
The impact of the Flexner report was felt around the world and changed the way every major nation taught medicine. In the United States, the two years of prerequisite university work gradually became a four-year degree as U.S. medical schools saw themselves as terminal degree granting intuitions with the M.D. equivalent to a terminal doctorate such as the Ph.D. Whereas many European and British Empire medical schools saw physicians as a vocation, and as such not a terminal degree but rather an extended bachelor’s degree. Additionally, there was a push by the AMA for further physician clout as the premier, educated healer—mainly as a pushback against the atrocious reputation physicians previously enjoyed, and to set the allopathic, and later osteopathic, medical field apart from “lesser” fields such as chiropractors, naturopaths, and homeopaths.
Sources: Flexner Report
Flexner Report Summary on Wikipedia
Personal Experience as a Medical Student