well, I haven't read through the whole topic (mainly because it seems that half of it is arguing) so please excuse me if someone has already presented this theory.

From my personal experience, I believe we have dreams nearly all night. I believe during REM dreams are most vivid and easier to remember simply because of the eye movement. this may change during lucid dreams since you are concious (I have yet to experience true lucidity so I am not sure.) Since eye movement is something that you always do, even as you read this , you are more likely to remember, and since there is little to no eye movement in other stages then you may not remember well.