Writing Out Daydreams and Sticking to It

   
    Some people have the incredible gift of always being able to write at a considerably swift pace. I am not one of them.
   However, like most people, I can daydream with the ease of snapping my fingers, and the rapidity of blinking my eyes. And since I daydream quite a bit, I try to write some of them down as stand-alone scenes or short stories.
    But it doesn't always work out very well. I've found myself abandoning the effort on more than one occasion, (sometimes just after the first few sentences) because it's become boring. I can't type as fast as I can picture something, which makes the scene go a lot slower than it did in my mind, and that gets frustrating. I end up losing interest in the whole story and just move on to something else.
    This isn't horrible, but I'd really like to be able to stick to writing goals like it, so developing an effective solution would be nice.

To me, daydreams are kind of like blurry pictures of a scene;
they're legible, but a tad blurry (like this shaky picture I took),
and writing can make it much more clear and detailed.

    Daydreams are great creative exercises, sources of great story ideas, and it's just plain fun to do. But if I only focus on daydreaming as something fun, that's probably all that will come from it: momentary entertainment. And if I've already had fun with the daydream by the time I sit down to write about it, taking the extra time and effort to recreate and translate it into words would just feel pointless. The entertainment purpose has already been fulfilled, and without another motivation, there'd be  no reason to stick to writing it down.
    So there's got to be more than one purpose in daydreams that are intended to be written; something aside from having immediate amusement. Something that'll keep a person committed, determined to finishing it on the page. Writing the story for another person to enjoy could do the trick, or wanting to write the scene because it illustrates a point/cause really well. Or writing it down so that the daydream could be preserved and re-experienced without any alterations or missing events. These motivations can make good purposes, right?
    What do you think? Do you daydream a lot? Do you try to write them down? Have you ever had trouble doing it?