The Amabrush was a successfully-Kickstarted hands-free toothbrush that never actually shipped. Now another design for an automatic toothbrush, the CHIIZ, has been successfully Kickstarted, and perhaps they'll have better luck.
Since the CHIIZ doesn't have the protrusion in the front of it like the Amabrush did, that means you can actually shave and brush your teeth at the same time:
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But if you really want to save time, you should simultaneously shave and use the CHIIZ while taking a pee in the shower and listening to a motivational audiobook. Five times the efficiency!