I don't think you could be wrong about everything I have put in bold. Don't take this as an attack on your personal self, but here on SDN myself and many others try to put forth the most up-to-date and accurate advice we possibly can. While your experience may have been terrible, this is by no means how most D.O.s feel. Every single physician that is practicing today has been in our shoes and each and every one of them know the struggle that goes on with trying to obtain good LORs. The physicians who wrote me my letter literally jumped to the opportunity to write me a letter before I even had a chance to ask. Also, I find it almost laughable when you say "It's a major inconvenience to explain things all day to someone that knows literally nothing, and most likely won't even get into medical school.." Physicians are life long scholars who are skilled in the ways of teaching. Everyday a physician goes to work they are almost guaranteed to spend at least some minuscule amount of time teaching a resident new techniques or teaching a patient about an illness, etc. Also, if you are taking it upon yourself to shadow and you are actually taking it seriously, I would be willing to bet the odds are in your favor for a medical school acceptance. I highly doubt a physician would discount a pre-med student so easily.
My opinion: When I first found my passion for medicine I was lucky enough to know a nurse whom was very good friends with an osteopathic Plastic and Reconstructive Surgeon. This surgeon was one of the nicest ladies I have ever met and after I finished shadowing her for a full day she reached out to me and gave me her number just in case I felt the desire to shadow her or some of the other doctors she was in contact with. Osteopathic physicians, heck, every physician I have came in contact with while shadowing basically took me under their wing to show and teach to me as much as they possibly could in the short period of time I was around. Like I said above, when I was shadowing another D.O. he was telling me about his experience with applying to medical school and before I knew it he was jumping at offering to write me a LOR. It is ignorant to believe that every physician thinks pre-meds are annoying, set-up to fail, and "literally know nothing," but if this is how you feel then I am sorry you had to drive a whopping 800 miles for a letter. That is insane and I would never do that. What school did you get accepted in to?