VAG experimented with electrically adjusted variable-displacement oil and water pumps, which they patented.
From the Audi patent of 2011:
"Smaller in terms of delivery rate, these volumetric-flow-controlled oil pumps operate only as required, and no longer need to circulate oil continuously.
These regulated pumps switch from the low to the high pressure stage either at a defined engine speed or in a continuously variable fashion, depending on the design. If the design includes spray jets for cooling the piston crown, they are activated at this point. Variable operation is possible with both of the common designs: gear pumps and vane pumps. A number of methods can be used to switch the pump between stages – an electrohydraulic mechanism, for example."
The logic of an electric water pump is that driving the pump at high rpm when not needed just wastes horsepower. If the pump could be made to run intermittently and controlled by ECU, it should run faster when the coolant is hot and not at all when it's cold. On a start-stop engine this is vital: electric water pumps keep the coolant circulating during stops, preventing the damage that comes with excess heat building up in engine block and head.
An electric oil pump on the other side should need to be far more powerful than a water pump, drawing a lot of amps to move viscous oil. So they leave the pump to be driven by the crankshaft and increase or decrease the displacement as needed via an electrohydraulic actuator.