Earlier quoted context omitted.
Drug approvals are currently much better than nutrition studies. Your suggestion of allowing not-known-to-work "medicine" to be sold would return us to the era of patent medicines, which killed a lot of people. You can look at the supplements market to see people dying from a similar policy right now.
Like anything else, you have to look at both costs and benefits of the alternatives. The current extremely tough FDA approval process has the benefit you mention: Fewer people are injured by unsafe drugs. But it also has a big (but harder to observe) cost: If disease X kills 1000 people/year, then each year a cure is delayed kills 1000 people. The main argument against the current system is that it weighs the deaths…
So we already have experience with some alternatives to the current scheme.