The degree is for his/her own benefit. What I care about is whether the doctor is smart and well-informed.
No, I don't think that earning the right to use the suffix "M.D." means that the doctor is well-informed and knowledgeable.
With a self-taught doctor, you just have the questions that you ask to help you judge. With a doctor who's been through school, you have both your questions and the fact that he/she has been through what has been set out by the school issuing the degree.
Here are 5 freely available introductory calculus books.
Areas differ, as always. There's an amazing amount of philosophy out there for free, for example. (I was recently impressed to see how much of Sextus Empiricus was available, and works on the Pyrrhonian skeptics in general.)
Sure you can buy the same textbooks and push yourself through them, but I'm 100% sure it would have taken me longer than 4 years to learn as much on my own as I did in college that was directly relevant to my day to day job. I'm not even sure if I could have gotten through the high end math without a lot of help.
Would you like a self taught doctor over one with a degree?