The solution to this is to ban by default, and put the onus on the company developing the solution to prove it is safe. There are many drawbacks to this, BUT it does address the root cause of your concern.
Not really, that's damn near impossible. There's almost no way to prove an exhaustive negative, and to get close is insanely expensive. As an admittedly imperfect analogy, take a look at how expensive it is to get a drug to market (currently ~$2.5B [1]) in large part because you have to prove so much about how it works and how little harm it causes.
BTW Most of these compounds ARE tested for safety, just in a far more limited way. Proving things never cause harm is an entirely different bar.
I don't think it's impossible if the standard for "do no harm" was specified very rigorously.
Also I'd be interested to see if it's possible to make it an adversarial process, similar to how corporations define risks to shareholders. They can specify whatever risks they feel are correct, but if something happens that they didn't account for in their risks, they are liable for large compensation penalties to shareholders. Thus companies are incentivized to report every possible and conceivable risk to their business. Now to bring it back to the drugs example, have corporations specify on their own what "do no harm" looks like. And if it turns out the drug does impact something they never specify, have a penalty proportional to their revenue or market cap applied.
