There are probably hundreds of reasons why you'd want an intermediate surface, but I'll name a couple:
I've used it heavily for keeping track of fog-of-war. Each side has its own surface created the same size as the real battlefield. A black pixel on that surface means they haven't seen that pixel on the real battlefield, grey means they have, but can't anymore, and white means they can see that pixel right now. Using PF's shader, I can just blit that image on top of the composite image of the battlefield with all of the units on it, and the fog-of-war is complete. It's quite fast, but not fast enough that it could be run each frame.
I use intermediate images in Dr. Pocket as well. First, I load up the possible backgrounds, which are also used randomly as backgrounds for the menu screens. But for the play screen, I take the background selected by the user, darken parts of it, add the bottle, score/high-score box, time box, etc. and have the new play screen background all stored on a temporary surface. It saves A LOT of time to just blit that one full-screen image each frame, rather than blitting a full-screen background, darkening about 75% of it, and then applying an almost-full-screen overlay on top of that each frame. (That doesn't count the actual data, like viruses, pills, scores and time.)
You may want one image file/resource/etc, and pre-render other images based off of it for speed/memory efficiency. For example, pixel shaders... Do you want to modify the original image with them? Probably not, and you probably don't want to run the pixel shader every frame in realtime... Solution, blit the original image to an intermediate surface, use the pixel shaders on that surface, and then use that new surface when you blit to the backbuffer. These are games. Speed is important.
In any case where you want to have a flexible image on hand, and it doesn't come from a resource or file (hence it being flexible), most likely you'll need to have it stored on an intermediate surface... unless you want to bloat the installation package with all of the possible image combinations... which of course none of us want to do.
Hope this helps,
-John
