Why would the US government want to take him alive in the first place?

He's a potential hazard everywhere he goes. There are cases of home-grown terrorists in the US and Canada. There exists possibilities of people rescuing him if they brought him to trial in the US, despite how slim they might be and his capture/detainment would only anger the Islamic extremists.

Assassinating him was the best course of action, along with the DNA-testings and the proper Muslim burial to avoid any shrine establishments and more insult to Islamic beliefs.