I ran my bikes that way for quite a while. LH friction shifter and RH dropper remote on the geared bikes and, of course, just the remote on my single speeds - the Fox DOSS is fantastically adaptable that way as is the CrankBrothers remote. Absolutely it was my preference to run the dropper on the right hand to the point that my Explosif Ti frame is drilled (Stealth routing) to run that way.
It ended up being too hard to switch back and forth and also most remotes now are dedicated LH shifter style.
Sept. 13, 2020, 5:52 p.m. - Andrew Major
  I ran my bikes that way for quite a while. LH friction shifter and RH dropper remote on the geared bikes and, of course, just the remote on my single speeds - the Fox DOSS is fantastically adaptable that way as is the CrankBrothers remote. Absolutely it was my preference to run the dropper on the right hand to the point that my Explosif Ti frame is drilled (Stealth routing) to run that way. It ended up being too hard to switch back and forth and also most remotes now are dedicated LH shifter style.