The shots I showed, where I am 'dragging the shutter' are a combination of both flash exposure and ambient exposure. Because the background is exposed by ambient, the maximum aperture can be important to the shot. That's really all I am saying.
Some people in this thread were implying that if you are using flash then the aperture only matters for DOF. I felt in necessary to point out that aperture can also be important for blended exposures.
I will also cheerfully admit that blended exposure (flash + ambient) reduces demand for fast lenses. For one thing, you can get away with pretty slow shutter speeds. The flash will freeze the subjects (so long as they are not moving really fast) and the background is OOF anyway. Second, you must underexpose the subject/background by at least one stop so that the flash is more than just fill. This again reduces the needed exposure.
Back to my examples - I shot this ISO1600, f/4 and 1/25 and the ambient is underexposed by 1 and 1/3 stops.
To shoot this without flash I would have wanted a shutter speed of 1/125, so I need to find a total of 3 and 2/3 stops more light between the aperture and the ISO to both increase the shutter speed and also have the correct exposure.
So that's ISO3200, 1/125 and f/1.6
And of course, that shot at the table would never have worked at f/1.6.
So what am I concluding.....aperture sometimes matters with flash, but less than when shooting ambient. And combining ambient and flash can really let you get away with slower apertures (gain DOF when needed) in low light.