I'm going to focus on the power aspect of asynchronous design, since this is what the Potato Processor illustrates. There are two main arguments for low power consumption in asynchronous processors. Since there is no clock, the chip is entirely idle when there is no data, and then it draws very little power. The second reason, which is actually the reason which is most important to us here, is that asynchronous (delay-insensitive) circuits adjust their operating speed to environmental conditions. This is a huge advantage. We don't need to carry out complex trials and statistical guesswork to figure out what voltage and clock speed we should run our chips at in order to leave an appropriate margin. In a clocked system, we would have to adjust the clock to run slower if we turn down the voltage of the power supply.
The self-regulating power supply allows us to operate the delay-insensitive processor from just about any power source that is capable of providing approximately fifty microwatts of power at 0.8 volts. The speed of computation adjusts itself to the amount of power available.