> the "case" dataset will be highly polluted with control samples, which will no doubt turn up null results
You seem to be assuming the answer to the research here. It's true that polluting the "case" dataset with control samples will make it hard to find patterns/results. But polluting the control dataset with "case" samples causes exactly the same problem.
I would suggest that we'll need lots of studies with different groupings
> a bunch of other animals as "dogs" just because they want to be called dogs
I am not suggesting that we consider people autistic because they want to be autistic. I am suggesting that a lot of the people with "mild" autism seem to have very similar symptoms and subjective experiences to those with "severe" autism (even though it presents very differently). And that it is not at all obvious that the underlying cause is different.
The analogy I would use is that of a noise in the environment. Suppose there is a high pitched whining noise, but it's fairly quiet. That would likely be annoying, but wouldn't majorly affect you. Now suppose the it's louder, akin to a loud concert. That would probably be ok for a while or some of the time, but after a while it would start to get to you and might make you irritable or more tired. Now suppose the noise was really loud, like standing next to a jet engine loud. This would be utterly intolerable and completely debilitating. The cause of the problem in each of these cases is similar, the difference is just the degree of loudness.
And different profiles of Autism could well be similar, having a similar underlying cause despite wildly different presentations. Given that there is evidence that one of the main aspects of Autism is differences in sensory processing this analogy might even be quite literal.