The reasons we as officials don’t chase the ball is we don’t take our eyes off the players. We need at least one (two if there is three officials!) set of eyes on the players at all times.
If I’m in a two man game, my partner calls a foul and is reporting it to the table while I’m chasing the ball. then we have a shove, push or punch, fight, or anything who is going to see that if we are worried about the ball. The ball is the least of my worries when calling. And if by some chance we lose that ball, they will find one to replace it.
I have never seen a player retrieve a ball, and before he gets back the official quick start the play.
As far as two and three officials I will leave this. The average age of officials is raising every year, while the age of the players never change. Let that sink in. There is more officials over the age of 50, than under the age of thirty.
Over 70 percent of officials never last longer than two seasons. The number one reason for leaving is verbal abuse.
The game is getting faster and faster (fundamentals aren’t keeping up either) and you want to take one official off, and expect two older guys (who even if in shape are not going to keep up with 16-18 year olds without a sub for an entire game.)to cover more areas while complaining about them anticipating and being out of position in three man? How many players play the entire 32 minutes?