This is one of those topics that always causes back and forth arguments, both that have some valid points.
Personally, I have never had any bad reaction to aspartame and neither have my children. Both my children were big babies prone to being "chunky" long before anything artificial was on the cards, and I was starting to get scrutinised by health care professionals who possibly assumed I was feeding them buckets of chips in their highchair.
For this reason I made the decision to use sugar free drinks where non water drinks were not used. So while my friends were giving apple juice, I was giving sugar free squash (very diluted), when they weren't having water for whatever reason.
Over the course of a few years, this added up to quite a significant reduction in their calorie intake without any major compromise to what they received in terms of nutrition. This, along with an otherwise healthy diet, would have contributed to them "growing into their weight" faster than if I hadn't.
I too find some sugar free or reduced sugar products useful in maintaining my weight, and in fact controlling my appetite. I dispute the fact that sugar free gives the same insulin response to sugar, as mentioned upthread - they simply do not have the same effect on blood sugar as backed up by evidence based research and peer reviewed studies.
Unless myself or my child reacts to one of these products, I will continue to use them, and unless the official advice in this country changes, I will continue to trust that they are safe. I don't buy into conspiracy theories though if anecdotally somebody has an issue then of course they should discontinue use. I know a person who gets sent loopy by tomatoes.
Having said all that, the fact that I have found them useful, as well as many others, makes me feel it is not at all unreasonable for Change 4 Life to suggest them as an option. Of course water is better, of course moderation is fine, however there are those out there who don't even know where to start, and it really is a perfectly fine place to start if your diet is packed with sugar.
An extreme example is a show I was watching the other night with a 32 stone young woman who was drinking at least 2 x 1.5 litre bottles of full sugar coke every day. That's 1260 calories a day she could save by switching to diet coke and in terms of calorie deficit would initially trigger a 2 pound a week weight loss, not taking into account her massive weight which would probably cause it to be more. Of course she should drink water, but would that be likely?
Change 4 Life campaigns annoy me anyway for much less reasonable reasons than anything the OP has mentioned, and I can't quite put my finger on why. so OP YANBU, but I thought I'd share my views of sugar free from the perspective of someone who has no issue with them and why I haven't followed the increasingly popular aspartame-hating club.