The example shown is a lift fan in a single engine craft where I can see advantages in efficiency. It would allow you to dynamically vary the lift/thrust balance as required (most single engine cruising craft waste quite a bit of power on unneeded lift at higher engine rpm).
One of my craft (UH18) has a variable speed lift fan (manually controlled) and it is very handy at times. You can back off the lift fan speed and recover probably another 10hp or so for thrust at high engine speeds (you can also increase lift to cope with difficult surface conditions without too much thrust). It is a very simple variable speed belt drive system (variator) and, unlike the variable pitch design shown here, is well-proven (it has been used in lawn tractors, combine harversters, etc for over 60 years).