The problem is that most of the effects can look very, very different depending on what settings you tweak. Take Fractal Noise for example. What sort of thumbnail would you show? You can make it look vastly different when you tweak the settings. What would you show for Caustics? What about the majority of the color correction effects?
The thing is, with AE, the power comes in when you tweak the heck out of effects, stack them on top of each other, and use them to drive each other. (And then add some more layers on top of it.) What point is Wave World unless it's driving another effect? What use is Compound Blur without a driving precomp?
Check out this experiment using the Radio Waves effect:
Check out more experiments like that here: http://motionworks.net/after-effects-experiment-2/
How under-served would Radio Waves be if the thumbnail for it was just this?
In After Effects Help, we used to have an "Effect Galleries" section that tried to do this, but it failed for the reasons that Szalam mentions. Go to the "Effect Galleries" section here to see what I'm referring to:
But we removed that section because it didn't actually help in any real way, since there's no way to show all of the possibilities and uses for an effect with a simple static image or two---or even a preview movie.
There are still images that demonstrate some of the effects in the respective reference sections of After Effects Help, which you can see in various sections here: