If that were to happen, we can expect that the drug market would become like the supplement market: full of pseudo-science and products that do nothing. Right now, supplement makers are prohibited from making specific medical claims; they can say something like "gives you energy," but they can't say "cures cancer." The only reason they don't is because they legally can't. (And even then they sometimes do, and sometimes get away with it.) If they were suddenly allowed to, we would not get a flood of new drugs from the current pharmaceutical companies. We would get a flood of sugar pills from the current supplement companies.
The "since" part of the paragraph is also a bit of non-sequitur. Before and after the 1962 provision, drug companies had to prove safety, so it's not a surprise the death rate from drug toxicity stayed constant. Proving efficacy is about preventing companies from exploiting the public by selling stuff that has no hope of ever working as advertised.
The blind spot of proposals like this is that they assume good-faith actors acting rationally. They completely ignore bad-faith actors willing to sociopathically exploit people.