I don't think you understand how medicine works. Doctors have to train hard to diagnose correctly and provide a solution to the diagnosis (You say misdiagnosis happens all the time but this is a fallacy. For every case of misdiagnosis that has a bad outcome such as death there are hundreds, if not not thousands, of correct diagnoses, the difference being that the incorrect diagnoses are the only ones you hear about). Your opinion that doctors have no accountability is also a complete load of bollocks. If people die, the health body will want to know why, assuming you're living in a country with even an ounce of regulation. Fuck, even if it doesn't have a regulatory body because you're living somewhere like somalia, the family of the deceased are gonna be pretty fucking pissed too.
You also don't seem to understand how the free market works. The market only works because experts in their field have the knowledge and foresight to put shit into practice and do it correctly, as well as at an effective cost or rate of return. Getting together a bunch of idiots with no information about how to do anything and then suggesting that they could somehow do the same thing is a load of bunk. It's like suggesting that you could replace one expert in rocket science with 200 farmers and expect them to be able to solve equations about throat diameter and stagnation points on rocket engines from first principles.
Your "fact" about Wikipedia is also pretty much a lie. Wikipedia at this point is considered terrible by most educational institutions, and infact several of my friends at universities have reported that even citing wikipedia as a reliable source of information is likely to get that paper failed (at my universitiy it doesn't count as a fail but they do discard the information you obtained from it). I mean fuck, this can be demonstrated quite neatly by the fact that discussion pages about anime and the colour of ball hair are more popular and longer than articles on serious subjects such as Lift, Drag and Gravity or Medical conditions (which I note, have only been discovered, named, diagnosed and figured out by experts in medicine. I mean fuck, the article on "human assholes" actually had one of the longest discussions of all times because so many people deemed it important to argue about which picture of a human butt should be used on the article.
Firstly, many of the issues you identified are CAUSED by the lack of a free market: in EDUCATION. If there was a free market in education, you wouldn't have the problem of the select few monopolising everything (monopolies are impossible in a free market).
Medicine is particularly bad field for this, the AMA acts like the most bullying strongarm union there is, competent medical professionals are NOT ALLOWED to call themselves 'Doctors' just because they haven't paid their union dues aka med 'school' fees. These college courses you insist upon are little more than madrassas for big pharma... Opening up the healthcare to the free market with my cryptohealthcare scheme will:
1. Enhance CHOICE and quality of care. All your traditional doctors will still be around, plus there will be more alternative practictioners. Increasing choice can ONLY improve the quality of healthcare available.
2. Encourage INNOVATION. Significant medical advances made these days are often borrowed from tribal societies (e.g. ear candling, reiki). However these therapies are treated with disdain and slander by the doctors who see them only as a threat to their profit margins! People should be able to CHOOSE which practictioner to use without the government propagandising for one group.