The trouble is that Saddam Hussein was very careful to make sure that no one had too much power in his country, apart from him. For instance, he basically had two parallel armies - the regular Army and the Republican Guard. Each with its own command structure and generals. His secret police unit was a third force, as were his regular police, a fourth force. Dividing his forces between four military commands ensured none of them were strong enough to overthrow him, but that means that none were strong enough to replace him when he goes. He did this everywhere with every sector, making sure no one was strong enough to challenge him or undermine him. He extended this to his very family, refusing to give either Uday or Qsay the go ahead as heir apparent - because if one was the heir apparent, that would be a challenge. He creates this giant cult of personality, Stalinist in nature, but refuses to let anyone else be a big figure.
The bottom line is that when Saddam goes, there is nobody but nobody in a position to step into his shoes. Instead, his regime is reduced to a collection of fiefdoms which can run things for a while, as long as they hold together. But he's the big Kahuna, no one else has his stature. So the regime drifts for a while, but in the end, Democracy rules.
I dunno. Before we invaded, Iraq was the most westernized society in the Arab world, very secular population, well educated, predominantly urban. They had a good chance of achieving Democracy on their own. At least as good a chance as Trujillo's Dominican Republic or Franco's Spain.
And yes, China after Mao just lead to more communist dictatorship. So what? Same thing happened in the Soviet Union after Stalin. Basically, Communist states differ from run of the mill dictatorships because the bureaucratize rule.
But if we look at the Soviet Union, what's interesting is how it all happened. The Post-Stalin politburo, a bunch of guys who had come up in WWII all steadily aged, and then started dying off - Brezhnev, then Gromyko, Andropov, in the end it was all sick old men. They finally aged out of power, and the guys who came after - Gorbachev and Yeltsin ushered in the end of the Soviet Empire and Russian democracy.
You go look at North Korea and Syria, you see the same thing. There's been a nominal transfer of power to the annointed sun, but its really the politburo running things and they're getting old. Assad's politburo were all associates of his dad. What's the average age of the Chinese high command? What happens when they lose their grip....