Even when reducing the pixel response time to shorter intervals, such as 2ms or 4ms, the typical LCD style of operation is still constrained with other limitations that would not allow to profit from the shorter pixel intervals as expected to reduce blurriness.
Typical LCD panels show each frame in a "sample-and-hold" manner, by which all the pixels on each frame are kept lighted for the whole duration of the cycle for that frame rate (16ms for 60fps), and at the very end of that cycle the crystals twist and turn in a rush to be ready and adapt to the next frame, which also brings full light with it. That is done even when the pixel could have restored itself faster at its own independent response time of 2, 4, 6, 8 ms depending on the design.
In other words, the blurriness is not always caused because the liquid crystal pixel response time is slow, but because there might not be a break of light in between frames.
Note that here you can capitalize from the comment I made earlier about frame refresh time ('Note that I am not saying "the timing that takes a full frame to be displayed", which is a different concept.')
As follows: The frame could be displayed really fast within the 16 ms period between frames, and still have the time to DISAPPEAR out of sight to show black or something else to interrupt light, rather than sit there fully lighted and on hold until is time for the next frame.
An important factor is that, to perceive continuous motion, the human eye expects the image frames to have breaks in between and interrupt the constant supply of light, so it might not be misinterpreted as increased blurriness.
The sample-and-hold approach for each frame does not provide for that break, and when the next frame needs to be shown the twist-and-turn of the liquid crystal pixels is done so quickly that is not seen as a light interruption.
While discussing this subject with Brian Berkeley, he confirmed the following:
"Hold type driving is used in LCD-TVs and in other matrix-addressed displays. Compare this type of driving with CRT displays, which are impulsively driven. In an impulsively driven display, the image is present only for a short period of time. By contrast, in a hold-type driven display like an LCD, the image is held throughout the entire frame period until next frame is written.
Hold-type driving is good for eliminating flicker and for getting maximum light output, but there is a drawback to hold-type driving for moving pictures. If an image is moving at a rate of, say, a few pixels per frame, then there is effectively a positional error in that the image position is correct for only a fraction of the frame.
To measure motion picture response time of an LCD panel, there is a metric called "MPRT", which literally stands for motion picture response time. MPRT is useful for comparing different LCD-TVs, but it is not so useful for comparing LCDs to other technologies, such as plasma displays, projection displays, or CRTs. As in g-g time, it is also good to have a lower MPRT score.
Important note: Having very small gray-to-gray response time does not solve this problem. Even if the g-g response time is 0, MPRT can still be too large to have blur-free images. Again, this is due to hold-type driving mentioned above. A low g-g LC response time is necessary, but not sufficient, for achieving a low MPRT score."
Another factor is the flicker-fusion threshold of our vision, which should be lower than the frame refresh rate of the display to perceive motion without flicker. That varies with each person, and is something similar to the rainbow effect of color wheels on 1-chip DLP engine designs, which most people do not notice, but some do.