This is a very open-ended and potentially opinionated question, but I'll do my best to answer.
If I understand your question right, what you refer to as "navigation controls at the top" is actually called the Android Action Bar.
The action bar is a window feature that identifies the user location, and provides user actions and navigation modes. Using the action bar offers your users a familiar interface across applications that the system gracefully adapts for different screen configurations.
The key word in that quote is window. The action bar not only contains things for the user to interact with, but serves as a buffer between the status bar and the app running, almost like a sill to a window. And by displaying the current activity at the top of the app, it serves as an introduction to the rest of the content.
Other reasons why the action bar is at the top:
- Drop-down lists
All of those elements would have to either appear from the top (relative to what without the action bar?) or display bottom-up, which would both look unappealing.
Finally, the actual Android on-screen navigation keys are at the bottom, as shown in your screenshot. Although it might be more accessible on larger screens if the action bar was at the bottom, having it right next to the navigation keys would make the interface look bottom-heavy. It also might create unintended actions from users, with the close proximity of so many elements.