What you're talking about is quite similar to letters of marque and reprisal.
The whole point of this is that currently, there is no due process. That is, an American citizen should at least be charged with treason, PUBLICLY, and not simply wiped out by Obama at his video game console.
If we want to develop some other process, that’s fine. But it’s got to be public, open, done in advance, and not at the whim of one person or a tiny group of people. (I’m only talking about the case of the killing of American citizens, btw.)
Ironically, Bambi & Co. don’t let the military fight; killing on the battlefield is practically forbidden, and defending yourself, if you’re a soldier, is a major no-no.
Furthermore, because of these misguided policies, some of these terrorists had been caught by the military earlier. They should have been killed or permanently locked up then, but they were treated as common criminals and turned over to their countries. They were then released by their countries and returned immediately to attack us. So Bambi is doing this to clean up the mess he has made of our battlefield policy, and probably to get rid of a few jihadis that may be a problem to his favorite, official jihadis.
But when it comes down to American citizens, we need a public process, not just one nutty individual’s decree.