Because it hasn't been established that al-Awlaki was an enemy soldier, or anything like it.

According to you. You keep forgetting that part.

So you don't have any problem at all with a government acting as judge, jury, and executioner with absolutely no public oversight?

In matters of war and national security? Nope. In fact, I wish we had the Official Secrets Act that they use in Britain and that the press was subject to D-notices.

Public oversight is precisely what gives governments that kind of authority.

No, monopoly of force does that.