If there were any market incentive whatsoever for that, it would already exist. The FDA does not have magical anticompetitive powers that make people care less. We have private and public postal services and railroads operating alongside each other.
The best case scenario is that there is enough market will to allow a lab to monopolize the market, leaving you with the same problems as today but with even less standing in the way of fraud, like companies just paying for good reviews. The realistic case is that no such testing would happen, just like it was before the FDA.
And the FDA is part of why there is no market for it. Note, for instance, tat the above-mentioned site reviews supplements, which don't have as many restrictions (and which do very much need these kinds of reviews).
> like companies just paying for good reviews
That would conflict with "respected review company", and leave an opportunity for a company that doesn't accept any kind of payment.
What kind of precedent is there for this pattern working successfully, long term, in any industry? 'Review companies' get sabotaged all the time if they were ever reliable at all. I sure wouldn't want to rely on one for medicine I give to my family if it was anything like relying on Yelp for a decent restaurant. I'm not at all convinced that the open market is a valid locale for these incentives - it seems to come with inherent conflict of interest.
Maybe it's reasonable for us to agree that some kinds of oversight are worth funding as a society without waiting for incentives to sprout up out of the ground.
To be explicitly clear, I also think it might be a good idea to have a government-funded review laboratory in this context. (I don't automatically think it would thereby be uncorruptible, or even harder to corrupt, but guaranteeing its existence seems important.) But there's a huge difference between "review" and "prohibit".
The best case scenario is that there is enough market will to allow a lab to monopolize the market, leaving you with the same problems as today but with even less standing in the way of fraud, like companies just paying for good reviews. The realistic case is that no such testing would happen, just like it was before the FDA.