No it is not since you use your HANDS for transporting the ball to a goal and and balls are by definition, a sphere or spherical object; american football balls are NOT spherical.
The ball must be kicked after each score and to start each half (and overtime). PATs (point after touchdown) are mandatory if no 2-point conversion rule is in place. All other kicks are...
Some might say, simply, "because they kick the football." But the real story is deeper. The origin of Gridiron (American football) is in the history of the world's most popular sport: Football...