Of course you can proof the safety of a chemical compound for human consumption (at least to the best of current technical abilities and within an acceptable margin of error). This is done for i.e. drugs thousands of times each year. Yes it costs money and time, but that is about the only serious objection. You could also go to a risk based model, where the burden of proof for groups of chemical compounds shifts based on experience with similar compounds, potential environmental impact, local and global measurements, etc.
The FDA approves medical treatments, many of which are chemicals. They approve treatments based largely on how effective it is as treatment. It's safety profile is studied and considered in a broader context. Many drugs approved by the FDA are incredibly blatantly unsafe. The FDA spends non-trival amounts of effort communicating risks associated with chemicals to doctors and patients.
Outside of this example, proving a negative on this scale is a 1000x larger problem than proving there are no leprechauns. No one has proven there are no leprechauns. It is logically possible to prove a negative, but we simply cannot observe all of the places a leprechaun might be hiding at the same time. The best thing we can do is list off all the places we know there are no leprechauns. This is very different than "proof".
Scientists show the safety by searching diligently for unsafety and not finding it.
That's not proof. A ten year drug trial may fail to show problems that take 20 years to surface, but that doesn't mean the drug is safe.
I suspect a lot of these chemicals fall into that hard-to-find-problems category. Only when they are an overwhelming part of our environment for decades or even generations will we start to understand the effects.
So this is not just a matter of money. It's a hard problem.