Okay, so "Slingshot Smashing" or "Pivot Smashing" is still called that when you use D-Smash instead of F-Smash, correct? If so, I would say that doing a Pivot D-Smash (and in some cases charging the Smash) is useful for a few reasons:
1) Longer range on the D-Smash thanks to the slide (obviously)
2) Unlike F-Smash, you will slide the duration of the D-Smash (after you stop charging it if you were). I have had someone try to Shield Grab me while I was doing this and I managed to slide so far that the back hit of D-Smash connected before his Grab came out.
3) If you charge the D-Smash, you stay very close to the ground while sliding, and can therefore duck under attacks (much like Crawling, though when timed right you can slide considerably faster than you can Crawl)
The third point raises a (highly situational) way to beat Falco's Reflector: run away from the Reflector and Pivot D-Smash. Charge the Smash to slide under the Reflector and let him have it once the Reflector is almost put away. While this works, the Falco would have to Reflector while you have no Banana in hand AND you'd have to get a near-perfect read (which is much harder to do without being able to bait it with a Banana).
There are plenty of other moves you can slide under like this, but I figured I'd mention Falco's Reflector since someone mentioned it. You can even slide under Wolf's U-Smash, for example.
I'll add Pivot Smashing to the Kongpendium later tonight. To make sure, what I'm describing IS Pivot Smashing, right (again, using D-Smash instead of F-Smash)? Please correct me if I'm wrong.