From my own experiences with my disorder, I find daydreaming is one of my primary problems. I can't seem to control what my mind is thinking about. If I can't get it to focus on what needs to be focused on, I'm powerless to do anything. I also have a great deal of trouble keeping my attention steadied. It constantly drifts from one topic to another. If I try really hard to focus on a task, even one that fascinates me, I have so much trouble that it takes a tremendous amount of effort. Even though I'm brilliant with Math - I came up with tons of easier, more efficient methods for stuff I learned in Math homeschooling - it's so tremendously difficult for me to do a Math problem. I can't write and process what I'm writting at the same time, because the act of writing distracts me, so I can't even write down my work and have to keep it all in my head. If I drift for even a second, I have to start the entire problem over again. For this reason, a single Algebra problem usually takes me about a month to complete.
The root of my severe insomnia problem is that I cannot focus my mind to get it to relax. Instead, it goes straight to my worries, and I can do nothing to change the subject. As I get more tired, the problems get worse. Eventually, I lose my ability to read in my head. Then, I have to read out loud. Eventually, I cannot even do this anymore because concentrating on translating the words into sounds distracts me from processing their meaning, so I can't even hear what I'm speaking. At that point, my only option is to use a screenreader, something I have a pitifully limited selection to choose from, and I'm very, very tired of pasting every single post on this forum into word when I'm like that just so I can find out what it says.
Once, I took a medication (I can find out what it was if anyone cares) that made the problem worse, and it really highlighted what it does. At one point during that time, it got so severe that I lost my ability to talk because my mind was going all over the place so fast. I actually became nonverbal. Though this only occured at the worst point of the medication and only briefly, I find it fascinating in that it's caused me to believe that this is why some aspies cannot talk, yet can type.
So to me, the idea that my brain not only drifts less, but that it doesn't drift at all, is completely obsurd. I know from experience that that just isn't the case.