Ben Ladin was a notorious bandit who'd murdered thousands of people. Any damned fool could see he could not be trusted. Turning him into meat at the first opportunity was not only a wise course of action it was demanded.
As far as justice what do you think would be easier. Would you rather be killed instantly or would you rather be paraded in front of people having to listen to testimony about how evil you are, be pronounced guilty and then have to wait until an appointed time, sweating it out until the noose is put about your neck and you are hanged before a world rejoicing over your death.
A quick death is too easy. A good trial is a cathartic for the whole world. A public death sets a much bigger example then someone killed in secret. It would be much harder for Islamic terrorist to forget as they understand one thing and that is strength. It takes strength and national charactor to give someone a fair trial and then sentence them to the death that they so richly deserve.