Our invasion of Iraq versus North Korea not being invaded shows that we only invade countries that don't really have WMD.
Actually I don't think the U.S. would've attacked North Korea if they were known not to have nuclear capabilities. Back in 1994, during the showdown, Clinton did briefly consider a military action, but changed his mind upon being advised by the military that while the U.S. and its allies would be victorious eventually, there's no way even a limited action wouldn't have escalated into a full-blown conflict in the peninsula, resulting in at least 100,000 American soldiers dead, not to mention millions of South Koreans and economic ruin. And this was when North Korea was actually isolated.
The same would probably go for Iran. Even with the regime's collapse, the U.S. would be locked in a bitter guerrilla war in a country that suits such kind of warfare perfectly (anyone claiming opponents of the regime would welcome U.S. troops as liberators is obviously a moron). So we're going to see serious, but indirect action, which, as pointed out above, may do harm to the state's economy in short term, but won't dislodge the regime.
It's kind of Orwellian that the extremists on both sides essentially are sustaining each other.