They are absolutely a part of the play. Arguably the most important part of the play. 95% of what determines which side is going to “win” the play happens in those presnap things. Especially once the West Coast Offense got invented. 3 and 5 step drops are all determined presnap, the QB reads the defense decided this guy will be open in this spot, snap, step step step, throw to spot.
The clock only stops on incompletions and out of bounds late in the 2nd and 4th quarters.
The NFL could, if they wanted to, go by play count. On average each team gets 60 offensive plays a game. So they could go to 120 plays a game. The problem with that model is it gets rid of the 2 minute drive.
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.