Two things do not seem to be in dispute. One, bin Laden said many times that he is at war with America. Two, bin Laden is a head of a terrorist group.
Therefore, if US declares a war on terrorism, bin Laden is a target.
If you have him in your "custody" and protect him, you place yourself at war with America. This is not justice, "American" or otherwise. This is not a criminal investigation. This is war.
>What tangible advantage does it have against OBL and his terrorist group after all these bombing?
If you still can't discern what advantages in the war on bin Laden we gained by helping Northern Aliance, I have to doubt your mental capabilities. Or your honesty.