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I guess I am not a purist. I grew up and played in the jump ball days, but hated the jump ball for the fact that when a small player tied up a much taller player, it was a pointless effort. It was pretty obvious who would get the ball. The jump ball, although a traditional rule, was the best thing ever eliminated from the rulebook. The jump favors one trait, height, and one skill, jumping, over all others.
In all other aspects of the game, you can compensate for height. Height on the boards can be neutralized by good blocking out, on offense by doubling the post, on offense by good ball movement and outisde shooting. In the jump ball, there is no way to neutralize height. The small guard who hustles to tie up the opposing center risks a foul and gains nothing off a held ball with the jump ball rule.
The AP gives what you have earned every time, and takes what you have lost every time. You get half a possession for every tie up, you lose half a possession every time you get tied up. That is the most fair resolution of the held ball situation, because neither team was able to assert complete control. You want the ball, get it completely. Get it halfway, that is what you really get - half a possession.
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