Is it fair to let your cat bite you after being overstimulated/annoyed by something you did?

My mainecoon cat is super sweet, and i usually avoid him getting overstimulated or annoyed by his behaviour. But sometimes if i see he is annoyed i put the side of my hand (chewy part below pinky) infront of his face and he launches at it and takes a moderately hard bite or two before being satisfied and then we continue like nothing happened. I do this as a way to say sorry instead of acting like it is bad of him to defend himself. Is this just dumb or is it fair to let him get his frustration out?