Flash sync at any shutter speed is a compelling advantage of the in-lens leaf shutter used in the Ricoh GR and certain other compact cameras. And an advantage in general of many fixed-lens compacts, that advantage being unavailable with interchangeable lens cameras*. Pro shooters know this well. A leaf shutter also has essentially zero vibration, unlike a focal plane shutter, all of which cause significant vibration.
Published in my review of the Ricoh GR in Guide to Mirrorless is a discussion of flash sync with the Ricoh GR and its relation to shutter speed and the built-in ND filter. The ideas apply to any similar camera.
The image below was shot at 1/1500 second using flash fill in order to keep the shadows from going completely black.
* It is possible to offer leaf shutter lenses as does Leica with the S line.
Oren G writes:
The Pentax Q system has interchangeable lenses with in-lens shutters that sync up to 1/2000 (as well as an electronic shutter function to allow use with non-shuttered lenses, e.g. adapted lenses). The "toy" lenses in the line don't have shutters, but the "real" ones - the fast normal prime and the zooms - do. As a product engineering achievement it's all the more remarkable because the lenses are *tiny* and featherweight.
Of course, neither the original Q/Q10 nor the slightly-larger-sensored Q7 would remotely meet your image quality requirements. So no practical implications for you, but just to keep the record technically correct.