Many drugs have passed FDA approval but later killed people. If the FDA were a private company, it might have gone out of business. But as a government monopoly, it's very hard to stop paying for. Between pharma companies, the government, and individual patients, the FDA has the least stake in the health of a particular patient.
UL is an example of a non-government organization that offers product safety certification. You see the UL seal on most consumer electric appliances. Imagine an FDA seal.
Drugs are not magical or special. They are a product like any other, and it is the consumer's right to choose a doctor, and for that doctor to choose proper medication. We regularly choose the best mechanics, plumbers, and other specialists we can find, and their reputation is partly a function of the type and quality of the parts and tools they use.