The purpose of a washing cup is to purify the hands. There are two handles on most washing cups. This allows us to avoid transmitting impurity from the unwashed hand to the washed hand by way of the wet, washed/pure hand touching the unwashed hand. With two handles, the pure hand can take the cup from the unwashed hand by using the handle that the unwashed hand is not holding, and then the washed hand can pour water on the unwashed/impure hand so both hands are pure. It would seem that to achieve the same effect with one handle, one would have to put the cup down and then pick it up again with the other hand. That seems cumbersome, at best.
Yet, I have seen one handled washing cups in some rather frum places.
Why would someone make or buy a one handled washing cup? Is there good halachic or practical reason for a one handle washing cup?