I agree that the mechanism you're suggesting is (by far!) the most plausible mechanism by which diet soda could potentially cause obesity. And certainly aspartame hits our tastebuds and this affects our brains (that's kinda the whole point) and we certainly don't understand the mechanism of anything that happens after that.
But... it's been tested and doesn't actually seem to happen in practice. http://orcid.org/0000-0003-3525-3473 If you have people drink artificially sweetened drinks vs. nothing, it doesn't seem to do anything. And—most important to me—if you have people substitute sugar-sweetened drinks for artificial sweeteners, this pretty clearly causes weight loss.
It's possible these are wrong, but I think that's the direction the evidence points to now. I wouldn't tell anyone to consume aspartame, but if you're thinking about substituting aspartame for sugar this seems like one of the easiest wins out there.