Why can't this trick make ground-based scopes as good as Hubble?

The noise introduced by atmospheric turbulence and pollution causes photos from the best ground telescopes to be much worse than from Hubble. Why not use simple noise-reduction techniques? Such as... take 100 digital photos of the same object and average them. The noise should cancel itself out. I know I'm wrong about this because if I can think of it, so can astronomers. Question: why am I wrong? Also, if you take a very long exposure photo from a ground-based scope (1 hr or more), why doesn't the atmospheric noise cancel itself out?