It doesn't say anything about its applications. I'm pretty sure there must exist some practical limitations. Theoretically it seems plausible that we can make the dipole spin continuously by switching the direction of external electric field. I'd like to know why this torque cannot be used to do mechanical work. Thanks!
It can and this kind of thing is used in MEMS micromechanical technology. The magnetic force on a current is a much more practical effect for electromechanical work production. One doesn't have to accumulate nett unbalanced charges on the rotor and the figures turn out to be much more practicable. It is only when the motor is very tiny and the torque needed very small that electrostatic motors become practicable. Also, the electromagnetic motor can use a split ring commutator to switch the field direction; there is no analogue for electric field. These days, however, with all kinds of technology to sense the rotor's angular position available, this last is a minor point.
You should calculate the torque you would get for practicable electric fields and charges and compare these with the Lorentz force on currents from practicable magnetic fields. That exercise more than any answer will show you the reasons for the lack of use of the idea aside from specialist fields, such as MEMS microactuation.
Electrostatic motors have been demonstrated since the 1700s (1st by Andrew Gordon and Benjamin Franklin). However, they usually need high voltages and are much more cumbersome to use than magnetic motors. See Wikipedia Electrostatic motors.