Apparently (according to a wikipedia page that says at the top it needs cleanup) there's some debate over whether SCT is a real disorder, and I'm not sure what the criteria would be among its critics.

In that debate a disorder is something that reduces effectiveness in daily life for people who are diagnosed with it. Fixing a disorder should improve people's daily lives. "Real" also means that it's not just an edge case of an existing disorder that's already in the book.

You also want the concept to pass some sanity checks. People diagnosed with the recently made up disorder of "internet addiction" for example didn't use the internet more than people without "internet addiction".

"What is a cognitive tempo, what does it mean for one to be sluggish?" The more clearly you can reduce it to brain function, the more "legitimate" it might be?

For that idea of "legitimate" our current way of diagnosing mental illnesses isn't legitimate. We made the categories we use today at a time before we knew much about the brain. Different people have different views about causes and the current system of labeling purposefully avoids focusing of causation. The DSM doesn't cite any studies that investigated real world causation to justify it's disease categories.

Are diagnoses "we can tell from [symptoms] you have [cluster] which we define by presence of [symptoms]" type tautologies or can you get any information out of them that you didn't already put in?

In practice that means that a psychologist gets payed by an insurance company to treat the disorder. Psychologist don't get payed for fixes something that's not in the DSM.

Drug are also tested on whether or not they treat a disease or disorder. Drugs only get FDA approval when the improve disorders.

If you take a drug to be happy and improve something that isn't a disorder that's illegal. If you take a drug to fix something that's recognized as a disorder, you are within the bounds of the law. At least that's the general idea.

I can remember venting to a psychiatrist that "depression is a description not an explanation and we still don't know what's wrong with me do we?"

Yes. But it's not clear that an explanation centered approach is helpful anyway. You don't get any benefit from having an explanation for being messed up. It might even be harmful because of self identity issues.