Both your vision and body must be engaged in a feedback loop to make any menu choice, however simple. A few sort-of solutions are in sight. They don't require locating the mouse on the screen. They help for some common tasks. But they aren't so good for other tasks.
Many vendors are sloppy about providing accelerators.
Keyboard accelerators may change depending on what is or isn't selected. And as my graphics program amply demonstrates, it often takes a ridiculous set of accelerators to reach the choice you want. Of course, those problems all assume that you actually know which accelerator you need. Accelerators are very useful for not having to switch between keyboard and mouse. They fall far short, however, of minimizing the attention we must pay to an interface.