You could do this, however it is very rare. Usually left wingers have a good left foot so they can stick crosses in quickly. If you are right footed and can't kick with your left you will always have to cut back which leaves more time for the ball to be taken off you. A manager/coach will not usually stick a right footer down the left unless he is stuck.
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it doesn't matter what foot u use as long as u get to thhe ball and anyway you should use both feet