In most of these types of stories, there is typically a little bit of truth that is blown out of proportion by someone.
Does aspartame have some side effects on some people? Yes. Are they as extensive and dangerous as the OP made it sound? No.
Should the FDA crack down on it? Frankly, the focus on such things is so skewed as to be almost comical, were it not so totally twisted that people's lives are affected every day by it. Think about it; liquor has a long list of well-documented health dangers, and is not only legal, it's treated almost like a cultural requirement for adult social interaction. Tobacco, likewise, would never make it on the market were it a new product introduced today, with the kinds of health risks it carries, and yet marijuana, which not only doesn't have such detrimental effects - and, in fact, has been demonstrated to have positive effects in medical use - is illegal.
Don't get me wrong; I'm not advocating a return to Prohibition and I do not support the cumulative "sin taxes" they keep passing on tobacco. I've never drank, never smoked (anything, either legal or not), and at almost fifty years old, I don't have any desire to start. I also don't have this big desire to play nanny on everyone else's health and well-being. If someone wants to smoke or drink, that's their business, not mine.
If someone wants to avoid aspartame, or if they want to suck down 3 liters of diet soda every day, then that's their choice.