Is there a good explanation why the sticky navigation is always on top of a mobile website and not at the bottom? I reckon that with bigger and bigger screens, as a user, you'd want the menu button in the thumb-safe region of the screen...
Through hierarchy and natural reading habits, we always read things from the top, which is generally where a website's title and menus are.
With respect to your question, menu buttons are still at the top, even for many mobile apps, regardless of convenience, but strictly due to hierarchy. Home, settings, etc, you always look for at the top.
This is not to say that nothing is put on the bottom. Facebook's app for example has three common buttons on the bottom: Status, Photo, and Check in, while the common Home, Messages, and Notifications are at the top.
While it may be better to have menus on the bottom for mobile users, the overhead in development would likely increase to compensate, and there is a high learning curve because people are not used to such things.