I don't have any physical limitation, but hardly ever use my rear brake. Only use it on steep and long downhills if worried that the front rim&brake might overheat and on sand or other loose surfaces where the front wheel would lock easily. Of course it's also good to have a second brake in the event of an equipment failure (such as a cable snapping) that disables the primary brake.
I'd be inclined to move the front brake cable to the right lever so it's operated by your better hand. And then have a second lever (bar-end shift lever is sometimes used for this on tandems) also operated by the right hand connected to the rear brake for use on long descents or if there's a mechanical issue with the main lever.