Just a guess:

Tree structures grow downward (root at top, leaves at bottom) because people read from the top of the page toward the bottom. Furthermore, if you were to draw a large tree that spanned several pages, it would be awkward to ask the reader to skip ahead a few pages and then work backward.

Furthermore, whether the convention started for the reason explained above or for some other reason, we continue the practice today exactly because it is a convention. We have corresponding terms like *top level node* (meaning the root) that wouldn't make as much sense if we drew the structure with the root at the bottom.