From the beginning, I have practiced (controlled draw and relax) and shot (≈ 2/3 left-handed, 1/3 right-handed) archery ambidextrously. I have severe spine, neck, and shoulder injuries. "Maintaining an even strain," to use a "Right Stuff" phrase, keeps me ambulatory. Side effects may include: ability to use bows that others cannot; slight possibility to reasonably take shots that others cannot; ability to try different bows and different styles of shooting with reasonable likelihood of decent results. There is no downside to ambidextrous shooting.
Hope this helps.