I am more thinking about tablets and convertibles. But even on a phone a similar concept could work: You summon the menu with some kind of gesture (for instance dragging over a screen edge). The menu pops up in the center of the screen and you can select an item with just a single directional swipe. If the selected item is a submenu and contains some child items, it will slide to the center of the screen and you can do another swipe to select one of the children.
So you could select an item extremely quickly with just two swipes. And there are already quite a few items at level two! If your top-level menu has eight submenu items and each submenu again contains seven items (+one to go back to the root) you have already 56 possible items in this menu. And you could select one of them in well beyond a second, even without looking at the screen!
So you could select an item extremely quickly with just two swipes. And there are already quite a few items at level two! If your top-level menu has eight submenu items and each submenu again contains seven items (+one to go back to the root) you have already 56 possible items in this menu. And you could select one of them in well beyond a second, even without looking at the screen!