It isn't.
But, is the wording in 4-15-2 saying the touch after the bat and before the ball hits the ground is simply "ending the legal dribble", or is it not permitted, and therefore a violation?
It's true it is not listed as a specific violation in Rule 9, but the second touch after a bat into the air is also not listed as a specific way to end the dribble, in 4-15-4. In just about any real-world play, doesn't the dribble end
after the ball has bounced?
Let's say A1 is standing in place, dribbling with their right hand. A1 then starts to push the ball towards the floor towards their left side, as if to start a drive to the left. After the ball leaves their right hand, but before the ball hits the floor, A1 bats the ball with their left hand to push it back towards the right. Is this a legal play? Or, in a Nevada-type play, (
) how many times can they bat it back and forth between their hands before it hits the ground? The batting doesn't meet meet any of the requirements of ending a dribble in 4-15-4.
That's why I believe they put in the wording of 4-15-2, to say once the ball has been batted/pushed to the floor, (or even up into the air), it must be permitted to hit the floor before the next touch.