I am 99.99% right-handed and, after an accident a few years ago, I was unable to use my right arm. Try as I might, I never learned to compensate over the many weeks of recuperation. Even the simplest task became almost impossible.
My sister, who was left-handed, went through usual "it's a bad habit and she must be trained out of it" scene during her school years. As a result, she ended up being ambidextrous and can not only write equally well with either hand (totally different handwriting though), she even had a party trick of writing with both hands at the same time. Used to make me feel queasy watching that.