On a mechanical level, a 4 year degree is an entrance requirement at med/law schools.
On a more practical level, the schools that are good enough to land you a job as a doctor/lawyer are all so competitive that a hole in your CV like not having a bachelor's degree when everyone else has one is a real disadvantage.
On the practical point, I suppose that's true. There are a few US universities that offer slightly shortened paths to getting a medical or law degree for students entering as undergraduates. I seem to recall that CUNY (City University of New York) offered a six-year B.S./M.D. program, and Columbia offered a six-year bachelor's/JD program, and maybe they still do, but of course you get a bachelor's degree during the course of such programs.
The requirement that one have a bachelor's degree prior to entering a first-degree law program gradually took hold, mainly during the earlier part of the 20th century I believe. One reason was to make it harder for people (particularly people from immigrant communities) to enter the legal profession. Another reason was to increase the prestige of the legal profession by turning it into a graduate degree program. This latter reason is also behind two later developments (making it standard for the law degree program to be 3 years, and rebranding the name of the degree from the traditional LLB (Bachelor of Laws) to the pretentious JD (Juris Doctor). The 3-year standardization was not fully in place until the mid-20th century, IINM, and the LLB->JD rebranding largely took place during the early post-WW2 era. The JD rebranding no doubt had something to do with the high prestige enjoyed by the medical profession by the mid-20th century.
As for why the bachelor's degree is required for medical schools, I don't know as much about that (I'm a lawyer and have studied the history of the US legal profession a bit). I suspect some of the reasons are the same (other than competition with the other profession, since I think the medical profession was the earlier mover here).
Edit: postwar -> post-WW2 as I realize most HN readers may not have grown up with that long-default US usage of "postwar".
Thanks - my wife is a solicitor in Scotland (and has been called to the Bar as an Advocate) and she did her LLB as a second degree as she already had a first degree. Although her route was unintentional it certainly used to be "traditional" to do law as second degree (and some universities here do an accelerated 2 year ordinary LLB) after a degree in classics or similar. She trained in the Civil Service as a solicitor (when you get a law degree you are still 3 years away from actually qualifying - you have to do a postgraduate course then do two years training in a a law firm) and their filtering criteria for trainees was that they have 2 first degrees....
Only a very small number of people do law as a second degree these days.
Amusingly, the process for training as an advocate is known as devilling - where you are apprenticed to a senior junior and during that time you are literally an advocate's devil :-)
I should add that we're starting to see some reverse movement in the US legal profession on this stuff, glacially speaking. The 3-year requirement for American Bar Association-accredited law schools has come increasingly into question during the past few years, partly a result of the current perceived crisis of historically high unemployment and lack of practical skills among (typically heavily-in-debt) law school graduates. A reduction from 3 to 2 years is foreseeable. In which case it may become marginally tougher to maintain that the degree should have the word 'Doctor' in it.
Edit: Another thing we're starting to hear in conjunction with calls to reduce the 3-year program is to institutionalize something like the 'devilling' that you speak of, i.e. to replace the third academic year with an apprenticeship year.
