6.02b is there to prevent the batter from stepping out of the box as the pitcher starts his pitch. It doesn't mean that a bater must remain in the box until he is put out or reaches base.
This has been discussed earlier and I beleive the consensus was that there's no reason to prevent a batter from exchanging his bat for another. However, if the batter attempted to do so too often (such as after each pitch), I'd be inclined to put a stop to it rather quickly. In my judgement that batter would be attempting to delay the game or make a travesty of the game.
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