This is based on a stupid idea that keyboard shortcuts are fast only because they are done on a keyboard. But this is simply false -- they are fast because they are simple gestures I can train and perform without thinking about it. Same applies to mouse -- in a well designed GUI, one can easily train to select an option or go through a dialog box with a blink of an eye.

Now, typing anything is just a complex procedure involving quite a lot of attention; what's worse, it cannot be trained since this HUD's response for a certain input will be mostly unpredictable depending of the state of its fuzzy AI. Not to mention that it additionally makes one constantly waste time on reading HUD window to check what action it is planning to execute.

Finally, when drawing or using any heavy mouse-dependent application one usually can fire keyboard shortcuts with one hand while the second is constantly holding mouse -- typing requires two hands, so it makes one waste additional time to grab the mouse back and re-adjust hand.