If poltergeists are the reason objects move and if they are spirits why don't they communicate instead of just moving things? Why not write a word or draw something on a wall for instance?
That would be way too easy. Besides the ghost theory, there is also the idea that poltergeists are somehow representations of built-up adolescent angst.
On a slightly related note, my ex would light candles on Halloween for Harry Houdini, per his request. He said that his greatest trick would be to find his way back from the dead on Halloween, and he needed the light to show him the way. One would think all those lit candles in all those households would be more confusing that helpful. My ex did not appreciate my logical nature.
The Creator Himself permanently set the boundaries that any demon or entity could get to without help. Ironically or sadly, people often increase what demons can do, still with the limits the Creator Himself set, but still often people hurt themselves and others.