While walking a custom unit on my project yesterday, I saw the wierdest sink I've ever seen (evidence to the right). The basin depth is less than 2".
At first it seems impossible to use, but then when you think about it, how often do you fill up the bathroom sink with water? The only difficulty I can think of is cleaning your toothpaste down the drain. It should come with one of those faucets that has a sprayer-head.