My mother sewed on my badges when I was a cub scout, but I did my own as a boy scout (and I ironed my uniform before every meeting.)
I think it should be a Tenderfoot Requirement to sew on your Scout badge.
We had a scout show up to Summer Camp with this Scout Badge in his pocket. I got out my sewing kit and taught him to sew, and he sewed on the badge. You should have seen the look on his face when he was done.
As far as I know, my son and he are the only ones in the troop who sew on their own badges.