According to Dean's biography, he got his medical degree in 1978, and he's been in politics since 1982, when he got elected to the Vermont statehouse.
This means a couple of things: number one, this guy was only actually a practicing medical doctor for about four years or so. Second of all, if he didn't quit drinking until 1981, this means that he was a drunk for a significant portion of the time he was actually a practicing medical doctor!
Yeah, this is a guy that should be President of the United States (eyeballs rolling up to the ceiling).
Something tells me that being a legislator in Vermont isn't exactly a full time job requiring someone to abandon their profession.
If what I have heard is correct, Dean became Governor when the then current Governor died in office (Dean was Lt. Governor). It is said that Dean got the news while he was in the midst of giving someone a physical; that he finished the physical and then got on the road to the capital. I'm fairly sure this was in 1991.
Feel free to correct me, but I think your premise is mired in a misunderstanding.