This amazes me still.
What purpose does the AP arrow serve?
It gives the team with the arrow the ball that has the arrow in a situation of a held ball, stuck ball, dual OOB violation, double foul/technical without team control, or accidental whistle without team control...I think I got them all.

The entire point is to award possession.
In our situation we just had one of those and team A
HAD the arrow.
The kicking of the ball,
BY RULE, ends the throw-in and switches the arrow. The purpose of the arrow was served, because it established possession and that possession
WAS NOT LOST by the kick.
Team B will still need another AP situation to use the arrow. By not switching you are actually taking a potential possession away from team B. A pretty strict penalty for a play that is really no different than knocking the ball OOB with any other part of the body.