I was reviewing this rule today, and perhaps I'm a little slow today but what am I missing here...If all the footballs have been examined, approved and marked for play, and during a series of downs the quarterback wants to change footballs, why not?

During a series a team cannot change between types of balls (leather, rubber, etc.) even if they have been approved. Only at the start of a series. So you can't play with the rubber ball in the rain and then bring in the leather ball to kick to the oppenents.
We seldom have a team give us different types of balls to approve at the start of a game.
And, to tell the truth, as long as the ball they bring in is legal, I'm not too worried about whether I approved it before or not.

Jim thank you. I misunderstood the rule as not being able to change footballs from one leather to another leather ball during a series of downs. Which didn't make much sense since footballs can often be rotated due to long incomplete passes from one down to the next. Regards.