While I'm sure this is true and there are real reasons why performing such experiments on yourself may be a very bad idea, there are few caveats.
First (which I don't really want to concentrate on) is that's why this is an experiment. People did stupid things (and sometimes died because of them) for entire human history and some hundreds of years later are remembered as "great scientists". Trying to monopolize research and experimentation around academia and "certified professionals" (certified by academia, that is) is a most despicable thing I can imagine. I see that this opinion is basically a point of conflict of two different political views, so there isn't much that can be said to (quickly) persuade someone, who does not feel like this in the first place, but I strongly feel that if people can be "free" in any sense at all, they really should be free to do whatever the fuck they want to themselves. If they wanna die, let them die. If they wanna do drugs, let them do drugs. If they wanna perform stupidly dangerous experiments over themselves, let them do that. If they wanna give somebody else a consent to perform a stupidly dangerous experiment over them — it's their prerogative.
Second is much less philosophical and much more grim. This probably depends on your environment quite a lot (country/place, level of income, connections), so take this as my subjective experience. The problem is that dealing with certified medical professionals performing FDA (or whatever) approved procedures over yourself sometimes feels pretty much as dangerous, if not more. You often have no idea what they are really doing to you, and it's sometimes blatantly obvious they don't really understand it either. Often it is not clear if the treatment (which might be totally safe and correct in some cases!) is adequate to your case, not much of analysis is performed and every little bit you have to do along the way costs quite a lot of money and/or prevents you from living normal life, leaving you quite miserable overall. And the more minor the thing you are trying to fix is, the worse it is. And the worst of it, it is pretty clear that your doctors don't really care. They are relatively safe (legally) if they are working by the book, so they are working by the book. And "the book" often happens to be a result of bureaucratic machine, not common sense. And, after all, they have seen (maybe just 30 minutes ago) people in much worse condition than yourself, so unless you are really dying, what's even the trouble? And all of it even when we ignore the fact, that "the book" and the status quo of the field changes all the time, much of recognized medical research lacks the quality you wish it'd had and accepted views today sometimes are vastly different than 20 years ago. And let's be honest: 20 years of "experience" is nothing, when we are talking about high-stake decision making on the frontiers of the scientific research (and whatever affects your health and well-being always feels like "high-stake").