I've seen some actual scientific papers discussing if it's possible aspartame and other non-nutrative sweeteners, like Stevia, and sugar alcohols, like Xylitol, Malitol, or Sucralose may still play a role in diabetes and obesity despite having no calories, or carbohydrates humans can metabolize.
The theory is that just TASTING sweet things sets off many of the same hormonal responses and chemical processes related to obesity and Type II Diabetes even though there's no actual caloric content. Or that it messes with your normal signals of hunger and satiety. Where the tongue says "yep we ate... not hungry" and the stomach says "What gives?" etc. and you wind up actually eating MORE in the long run.
At least some rats did when fed two batches of yogurt, one with glucose, the other saccharine.
However double blind studies in actual humans are tricky. Because it's a combination of metabolic, hormonal, and neurological/psychological factors. And I'm not sure which of these studies, if any, ever actually had test subjects secured to the point they could be fed a controlled and measured diet, given controlled levels of activity, or just relied on weighing, blood work, and self-reporting on questionnaires.
So I think it's possible that artificial sweeteners may actually be contributing to the "Obesity Epidemic" but even if that's so, I agree it's pretty clear they're in no way carcinogenic or toxic, save to a very rare subset of the population with certain metabolic disorders, like Phenylketonuria, and for the most part those folks know who they are.