How can you ever prove something doesn't have any negative impacts? You're trying to prove a negative. Would you be willing to further delay a new medication that can help people today, but may have some averse effects for a subset of people far in the future? This is what we went through with the mRNA vaccines. We have to look at the tradeoffs. If banning aspartame means we may potentially prevent some cases of autism, but at the definite cost of large increases in obesity, would that be worth it?
Aspartame and added sugar would both be scrutinized in this hypothetical future where we are bit more cautious.
The answer is to probably ban aspartame if there is good reason to believe it is harming us, and/or tax sugary drinks until their negative externalities on society are paid for.