Burger menu at the bottom

Burger menu has lots of drawbacks. They do not show a current menu item, they hide the main menu options and often it is not handy to reach them on the screen. However, in comparison to a standard “More” tab in the bottom bar, a Burger menu doesn't overlap a Context menu. What if we try to solve all these problems?

Link to the prototype:
http://share.framerjs.com/03i6pz8ja7xq/