well, "best" is subjective, but IMHO the best argument against it is that some companies would skip FDA altogether and try to go direct to market, and would use marketing tactics to undermine faith in the FDA and convince people that the lack of FDA approval doesn't matter.
Personally, I do think this would happen, but I think there are better ways to combat this than to use force of law to gatekeep which molecules people are legally allowed to put into their own bodies. We could (and should) still require them to provide evidence for any claims they make, and failure to provide evidence opens them up for liability. There are situations in which paternalism seems justified, but I think in this we've gone way overboard.
AFIAK FDA doesn't regulate what you, yourself, are legally allowed to consume but rather what companies are allowed to market as drugs and legally distribute as such.
For example you can bring your own non-FDA approved drugs with you to the US for personal consumption. I found the following document, section 9-2 covers this topic: https://www.fda.gov/media/71776/download?attachment
That's a fair point, although the FDA (IIUC) has power to say whether some drug must be gated behind a prescription or can be over the counter. For over-the-counter stuff I think you have a good point, but for prescription drugs (which I'm sure is all or nearly all of the interesting drugs) they are gatekeepers.
Personally, I do think this would happen, but I think there are better ways to combat this than to use force of law to gatekeep which molecules people are legally allowed to put into their own bodies. We could (and should) still require them to provide evidence for any claims they make, and failure to provide evidence opens them up for liability. There are situations in which paternalism seems justified, but I think in this we've gone way overboard.