I've been doing this for quite a while now -- started doing it for both badminton and tennis in the 1980s, I think. Prior to that, I've played 2-paddle ping pong for some 40 years. Switched to right arm in volleyball in the early 90s (because of a shoulder injury). As a lefty in a right-handed world I learned to do quite a lot of things right-handed with a fair to decent amount of competency.
Not sure that I'm really ambidextrous tho' -- I consider myself as functionally bi-lateral. For most skills I am still much better with my left had/arm than my right. This exception is (overhand) throwing and batting. While it appears that many lefties have learned to competently perform tasks with their right hand/arm, I have also come across quite a few righties that have been forced to learn to develop their left hand/arm. They have made the effort to develop the left side because of an auto accident or an injury (sometimes an overuse injury) to the right arm.
I'm sure that more ppl could accomplish this feat but most are not motivated enough to put in the effort.