The fact is that it is not ever possible to prove something safe, we can only say that it has not yet been shown to be dangerous.
When I was a kid, all kids' shoe stores had this gadget that you stuck your feet into in your new shoes, and could see the X-ray of your feet. It was great because the parents and shoe store people could see if the shoes fit well or not, and kids loved it (I certainly did!) to see their own bones wiggling. Can you imagine? Pregnant mothers of course, were in the store, brought their kids to the machine, etc. It was not considered dangerous. Now, of course, it is, and pregnant women are covered in lead aprons if they have to get x-rays, and people's exposure to x-ray radiation is controlled. Doctors hide behind lead screens while operating x-ray equipment.
And there are thousands of products, drugs and equipment that was not considered at all dangerous in the past but only because they hadn't yet discovered the danger.
Keep in mind, also, that sweeteners are a huge business. There isn't much motivation on the part of the producers of it to do extensive research on their safety. There's not much money to do it by other private, government or consumer groups. So we feed our kids tons of diet coke and other crap, and don't know what damage it might do. And it is insidiously in way too many things.
We may not know the dangers (maybe we already do, i don't know). But for sure we do a couple of damaging things by using it:
1. we get everyone (and kids most importantly) used to a constant high level of sweetness - it's hard for most kids to think of quenching their thirst if the liquid is not super-sweet.
2. we get people used to a very lousy taste of sweetness (aspartame and all the other sweeteners like saccharine, are horrible and leave a disgusting aftertaste) making our taste buds and our own appreciation of food become used to a very bad standard.
So why use it? It's possible to live without it. (I can understand a diabetic craving sweets and using it - I would - but outside of that extreme case, I'd stick to sugar, or less sweets.)
"Siduri said, 'Gilgamesh, where are you roaming? You will never find the eternal life that you seek...Savour your food, make each of your days a delight, ... let music and dancing fill your house, love the child who holds you by the hand and give your wife pleasure in your embrace.'"