Iraq is partially a lesson in that negative sense - that no, relying on leftist induced paralysis will not protect virulent anti-American regimes from the consequences of crossing us. It can also be a lesson in a positive sense - an example to peoples of the region that pro-western democracy is possible, that only their hardline rulers prevent it.
It also was done for more immediate, practical, military strategy reasons. It got our troops out of Saudi, where they are a threat to the regime's legitimacy, a recruiting poster for Bin Laden, and a regular terrorism target without really being able to fight back. It did so without losing control of the region, or cutting and running after the next Khobar Towers.
Strategically, along with Afghanistan it has divided a geographic bloc of terror supporting states that 2 years ago stretched from the borders of China clear to the Mediterrean coast. Syria is now isolated, entirely surrounded by pro-western states. Iran has pro-western forces stationed in several adjacent countries, where before it faced none.
These are not separate news stories. They are aspects of one overall strategy, to undermine the power of anti-western extremism and terrorism throughout the Islamic world. We are taking away billions in their funding, their accessible territories, their bases of recruitment, they ongoing political causes, their leaders.
Anyone might argue that we might have gotten away with doing less. But to not see what it is for or what good it does is willful blindness. Destroying entire hostile regimes transparently weakens our enemies.
Do we want to give them the same treatment? No, we'd rather avoid it.
That's the kind of "we're ready to dispose of you, but" kind of attitude that I was referring to. Back in WWII we didn't give Germany or Japan any hint we'd accept anything less than an unconditional surrender and the complete destruction of their armed forces - no hint whatsoever we'd negotiate peace beforehand. It amazes me how Libya's cave-in is being hailed as a great victory in the war on terror, when the other side of the story is we've decided to buy off a better-behaving rogue regime with rather limited WMD capability (compared to North Korea & Iran). Sure, Bush can talk all he wants about how the sanctions on Libya won't be lifted anytime soon, but it's crystal-clear a general thaw in relations was part of the deal. Not to mention Libya wasn't even included in the "axis of evil" to begin with.