Understanding voltage sampling rate of induction motors
It is not required to sample the voltage of a three phase machine at 4kHz.  The rate voltage measurements should be taken is dependent on what is being measured, and how "good" of a measurement is needed.

Without seeing the papers I can make an educated guess as to why you are seeing a 4kHz measurement rate.

Cheap oscilloscopes can easily sample at rates 1000 times 4kHz so the measurement is most likely not from an oscilloscope.  4kHz is well within the range of most commercial VFDs PWM frequency.  So I will guess that the machines in those papers are being driven by VFDs and the voltage measurements are being taken from VFD itself.

A VFD will sync its voltage measurement to its PWM to ensure the measurement is done when the node being measured is no being driven by the VFD, which would skew the measurement.  Also note that many VFDs do not directly measure the voltage applied to the motor cable, but calculate the voltage from entered machine information and the supplied current.