Thanks all, my initial thinking was:
1. Travel, as I remove one arm anyway, can I shoot as well without a second handle?
2. Adding the velcro strap would help with one hand
3. Slightly smaller footprint shooting vertically
4. Would definitely help with extreme close focus wide angle lighting (one light will be closer)
5. May feel unstable and awkward, particularly in stronger currents
6. One hand shooting without another handle can make shooting "from the hip" easier
7. One handing could also make light adjustments easier, with snooting. Being able to hold the snoot with one hand to make sml adjustments whilst keeping some distance from the viewfinder could be very beneficial.
8. Having your left hand free will allow you to more easily keep your camera in place whilst making small adjustments. The problem here is thay you'll only really be able to easily use your left hand but not your right...
One could argue that a lot of the one handing can be done with two handles and a strap though.