Firstly, the Colonial Marines would give it a major problem, because they appeared to have been disbanded and replaced with an inept 'United Systems Military', meaning that any portrayed outbreak would be contained and never found out about. I don't like that, any more than I like the fact that Whedon also cemented that Weyland-Yutani now no longer exists, but there we are.
Secondly, Iraq, no. Something with Israel and Palestinean terrorists would be just as likely to lure them, but any such film would have the same problem: Those who make it would be too tempted to make some sort of political commentry on it.
Thirdly, I don't see what 'Predator 3' would achieve. With the Aliens, there is always the knowledge that they at least want to try and escape and use anything living to breed with. Predators, though, regulate themselves. There is never any danger of them wanting to kill everyone in the world. The first worked because the entire situation was very contained, out in the middle of nowhere, but any film trying to repeat that would end up being a copy. The second went around in circles, because the police characters weere trying to figure out what was doing the killing when the audience already knew. 'Terminator 2' avoided stuff like that by having the Terminator make itself known, right from the start, but interjecting a completely new type it had to protect others from, compeltely shifting the dynamic.
You can't change the dynamic where there are Predators involved. Having it protect humans? Could you picture that working? What we're left with is just having it set up yet another hunt and there's only so many times that can be made fresh and even slightly entertaining.
'Alien Versus Predator' works by having the Aliens as a potentially uncontained threat. They fill the void the Predators refuse to, because they have rules. Aliens don't. They throw a situation into chaos and we see how this extraterrestrial hunter deals with that.
There are lots of things which can still be done with the threat the Aliens represent. Not so much Predators, alas. Where would the threat be? They won't take over the world. They'll only be interested in hunting a small group of individuals. If we go to where they come from, it'll just end up seeming like a film about Klingons. Do we want that? Truly?