There is no damn good reason to keep the clock running between plays in the NFL -- except to reduce the amount of playing time the NFL wants to see interrupting their 3+ hour TV commercials.
The clock only stops on incompletions and out of bounds late in the 2nd and 4th quarters.
You may want to do some research and bone up on your NFL rules.
There’s one very good reason to do it:
That’s how the game works
All sports rules are innately arbitrary. Why 100 yards? Why 4 plays to make 10 yards? Why 6 pts for a touchdown.
As for hockey the faceoff is part of the play, but there’s nothing going on with it. Not to the level of football. Nobody is moving around trying to get the other team to think they’re doing X.
I know my NFL rules just fine. Outside the 2 minute warning in the first half, and the last 5 minutes of the 2nd the only clock stoppage for out of bounds is until the ref spots the ball. Inside those windows it’s stopped until snap.