Why did they never released a photo of him? Why the commandos who did the raid died "mysteriously" in a helicopter crash a week later? ALL of them? THINK! If he was arrested it would be evidential that IT WAS NOT HIM. Yes, they should have arrested him, but that was just not possible...
By killing bin Laden, and not arresting him, the chance of a major attack to rescue him was not given to his associates. Granted, in the short term, attacks might rise. But, cutting the head off of Al-Qaida will throw them into confusion. After bin Laden, there is no inspirational leader to keep them together.
Put yourself in the viewpoint of the terrorists. If they kidnapped our military general, they would kill him in a heartbeat. Osama bin laden was a monster and deserved to die, plus it shows al Qaeda how serious America can be and how far we will go to avenge our citizens.
After September 11th, 2001, Osama Bin Laden went into hiding for 10 years. Would we have even been able to arrest him? Many efforts had already been made to bring him to justice, to no avail. He kept making videos that had nothing to do with surrendering, and probably had no intention of surrendering. We have to trust that our military did the right thing in the final search mission that brought him to justice.
I do not support capital punishment but Osama bin Laden was a special case. The American people would have itched for his death. Perhaps a trial and formal proceedings would have given him an opportunity to walk free. The events of 9-11 were so tragic, and so rare on American soil. If Osama bin Laden had been released, an American citizen would surely have assassinated him. Osama bin Laden's death was important to the survivors of 9-11 and their families. In that way, I think the right thing was done.
If Osama had been arrested, wherever he would have been held for interrogation would have been a huge target for terrorists. The legal wrangling over setting up any kind of trial would have consumed international politics, and an actual trial or tribunal would have frozen the world for months. No trial would have ever been anything but a guilty verdict, with a death sentence anyway.