Many people have comic-book logic in which the mere act of a trial is the difference between justice and vengeance. But this is “cargo cult” justice – tripe intended to make the hero seem morally superior.
The truth is that the only function of a trial is to ascertain guilt or innocence. The punishment is the part that brings about justice, and when there can be no doubt of guilt, there is no particular need for a trial. We have trials even in cases of “obvious” guilt because sometimes someone who is “obviously” guilty may in fact be innocent. But Osama bin Laden was at the point where there could never be even a shadow of doubt of guilt.
Bin Laden declared war on the United States. After treating the problem of al-Qaida as a police problem until the 9/11 attacks, Congress issued the Authorization for Use of Military Force, which is equivalent to a declaration of war. Bin Laden was killed as the head of al-Qaida in a military operation in a war zone. No need for judicial involvement, which is limited on the battlefield anyway. Admiral Yamamoto suffered a similar fate in World War II.
People who think there could be peace with radical Islam should read bin Laden’s “Letter to America” and see his demands. The short version: Everyone must convert to Islam, we must abolish our Constitution and govern our nation under Sharia law in every detail, including beheading, stoning, crucifixion, whipping, banning alcohol – the works.