Free throw violation -- why do we use the plane?
 

Just refreshing up on free throw violations and the thought occurred to me... why does the foot crossing the plane come into play with this rule but almost no other violation (out of bounds, backcourt, etc).

Any idea on the logic?

Also, the rule doesn't mention any other body part which is what you see more of -- players leaning into their opponent or putting their arm out extended over the other players box.

A lean will only improve your rebounding advantage marginally. A foot across the plane touching the floor only a jiffy after it legally may provides a much higher advantage to this team. Using the lane line plane as the threshold is the effort to keep free throw rebounding as equitable as possible.