The goal isn't to have multiple answers each containing a piece of the puzzle. It's to have a single, correct, comprehensive answer. Bounty provides a means of encouraging answers to tough problems by offering a reward: allowing you to subdivide this reward creates a situation where you're misleading those participating (who think they're competing for a big prize but only receive a portion of it) and potentially discouraging users from taking the time to write a complete answer.
In short, i think it's a terrible idea. Good, useful answers will be rewarded, by the voters who find them good and useful. If you aren't comfortable with the "winner takes all" bounty system, then just don't use it - there's no requirement that you do so ever.
