I don't think of "dragging the shutter" as only for intentionally getting blur, although that is a good reason. Sometimes if you have low ambient light, like a street scene or an interior, and need to light your subject with strobe, you could drag the shutter as stated to 1/15th second, simply to balance the light sources. You may want everything tack sharp, so you put the camera on a tripod.
In this wedding shot I wanted everything sharp, so I dragged the shutter to about 1/30 so the candles and fireplace would glow, and held the camera as steady as I could.
In the shot below, I was shooting a in niteclub, with very low ambient light, and built-in flash on the camera (with a slight warming gel over the flash). I recall setting the shutter speed at 1/4 so I could let the ambient "glow", but I also wanted a slow shutter speed to blurr the background to add some party atmosphere.
BTW, the model in the above shot is Rolando's buddy Carolina (this was from a couple years ago).
And RJ.... not all strobes have flash duration of 1/2000+. While on-camera stobes are fairly brief, my Normans can slow down to 1/350 of a second when powered all the way up, and if powered down, can be shorter.
Andy Pearlman Studio