No, no no, nooooo....
You can't be that stupid. You just can't.
Let me spell it out for you. First, it looks EXTREMELY bad for you to go stomping in, destabilize a country...no, TWO countries, then kick the sand off your boots, and walk away, saying "Well, it's your problem now." You made the mess, no matter how justified you feel you were in making it, you help fucking clean up.
Second, if someone came into your house, smashed it up, raped your wife, killed your dog, and hurt your kids, you'd kinda want to hurt him next time you saw him, right? Trash these people's country, and you don't look good to them. help them clean up, and while you may think it makes you look like a bleeding heart pussy liberal, but it also helps lower the potential for retaliation. Both for people abroad, and the troops you claim to support so very much. They have a hard enough time over there...you'd think you'd support anything that makes it even fractionally easier.
Thirdly, what conditions do you think help form an extremist? Do you think they just appear out of thin air? That they just wake up one day, and swear they'll risk their lives for a belief, for no particular reason? No, they are the disenfranchised, the poor, the uneducated. Those with nothing to lose anyways. You tear a country apart like you have, you make an extremist breeding ground.
So while stomping them into the dirt may make you feel like you have a bigger dick than the world, this way is the smarter way of doing things.