I just did some research on the history of the American football extra point. American football was derived from rugby for which carrying the ball over the touch line did not score any points but gave the team the opportunity to kick the ball between the posts for a score. When the player scored he placed the ball on the ground, which was referred to as the "touch down" and the team had to attempt the kick from that spot.
American football awarded poiints for crossing the goal line but also kept the kick attempt after the score for additional points. After various changes, it eventually resulted in the 6 pts for a TD as we have today and the single point after was kept for the purpose of trying to avoid ties as in the early days it wasn't so automatic.
Supposedly, part of the reason the NFL finally incorporated the 2-point conversion try was also to avoid ties (I personally don't see any valid data to support this as ties and eventually overtime games have been rare.). The purpose of adding excitement with the 2-point conversion seems to make more sense.