whyDoWeDrawThemThatWay

You can find the fruit by going down into the tree from the fruit in log n time, but it still takes me Linear time to grow. 

Are you looking for fruit in depth first search?

height-first search? Naaah

(pre-emptive "yes, I get the joke, I just choose to answer the question seriously anyway because I have nothing better to do")

Because they are just called "trees" because they have to be called something and "tree" makes for a nice memorable analogy. They aren't supposed to be trees and there is no particular reason to make them resemble real trees when drawing them. We traditionally read from top to bottom and for most kinds of data and algorithms it's more natural to start at the root than at the leaves, so to the top it goes.