I shot RH for 28 years and LH since 1996. I can shoot both ways but my mind likes to do flip-flops and turn inside out when I shoot RH -- I have to concentrate much more on the process as a righty. I had to shoot righty during a training I conducted in England on Nov. 22nd because there was no LH bow available.
I don't consider RH shooting as part of my hunting repertoire though.
Would it be handy not to have to turn in a tree stand to get the left shot, you bet. It takes a lot of effort to have nearly identical form on both sides which would be fairly important in order for the same arrow to work equally well LH and RH. As you know, it isn't just the dynamics of the bow and arrow that affect flight, our form is part of the formula also.
Finally, I am so fond of the graceful lines of standard recurve bows I wouldn't personally have any interest in boogering up those lines with an ambidextrous grip/bow shelf.