You do not want the left and right information in the center. There are 3 speakers up front for a reason - to separate the sound into a more realistic sound.
Think about an explosion that only occurs in the left channel. If you wire the left channel to the tweeter and the right channel to the woofers, you end up the explosion going to the tweeter and and nothing going to the woofers. So, you get just the high frequency part of the explosion in the center. And remember the center usually does not have as good base response as your main speakers. Plus, you would miss all the center speaker information.
Bi-wiring is there to bypass the crossover in the speaker, nothing more.
Think about an explosion that only occurs in the left channel. If you wire the left channel to the tweeter and the right channel to the woofers, you end up the explosion going to the tweeter and and nothing going to the woofers. So, you get just the high frequency part of the explosion in the center. And remember the center usually does not have as good base response as your main speakers. Plus, you would miss all the center speaker information.
Bi-wiring is there to bypass the crossover in the speaker, nothing more.