This is pretty much a myth. Since the surface area of the tape is no larger than the surface area of the flash itself, there is no real diffusion going on that will give us any practical improvement in light quality. All you are doing is forcing your strobe to work harder to produce the same amount of light, and maybe changing the color temperature of the light a little.
The same goes for an omni-bounce or plastic dome over a flash head. You may be simulating a bare bulb and sending light in all directions, but if you don't have a surface to bounce that light back onto your subject then it is being wasted. I giggle whenever I see someone using flash outside with it tilted up and a dome on it. I hope they brought extra batteries.
Back before modern TTL flashes when we were using manual strobes that didn't dial down the output well, the tape or handkerchief trick sometimes seemed to worked simply because it cut the output from the primitive flash units enough to balance it better with the lower available light.
My solution to the harshness of direct popup strobe, assuming you can't bounce it off a larger surface, is to slow my shutter speed and shoot closer to the level of the ambient light. You have to be careful because that can introduces a whole new set of problems including camera shake, subject movement and the mixing two different color temperature light sources. Still, I think the most common mistake made with direct flash is shooting too far above the available light. I try to shoot my popup flash no more than one f-stop above the available light unless that available light is really ugly.