I and many others at my company use special VFR more than most think simply because it is sometimes the only legal way to make certain things happen

Example:
Part 135 = NO IFR allowed into Class G airspace where there are no approaches. Our operation flies cargo into a small VFR ONLY Airport along the Coast and alot of our guys will use a nearby airport's approach to get down below the ceiling and once out of the clouds, request a VFR departure and fly VFR to our nearby VFR Only Airport. Since this nearby airport (the one with the Approach) is Class E down to the surface, we would need 3SM visibility to fly VFR in that airspace so, in order to fly lower than that, we can use Special VFR to get out of the Class E with 1 SM and Clear of Clouds and continue to our airport further up the coast which also only needs 1 SM and Clear of Clouds as well (Class G below 1,200ft agl Daytime)

As for a Part 91 (GA) Example, flying with a student down in FL, sometimes a rain storm will be so Isolated that it sometimes covers 1/2 of the airport (where the weather sensor is) and the other half (with a runway you could land on) is completely clear. We can use Special VFR here to enter the Class D because our Flight Visibility is at least 1 SM even though the reported weather may be way less than 1 SM.