No, I don't think it works that way. You can't just point at WMDs and say, "Here is the reason." It takes a media campaign. It takes lots and lots of distraction.
Saddam was an evil motherfucker and got what he deserved. But WMDs weren't the reason since he didn't have any. So, it was his murderous, dictatorial style of government, wasn't it? Perhaps. Then why him, and why then? Why not years before? Why not some other murderous dictator?
WMDs were the reason because he did have them. Clinton bombed Iraq in 1998 because he had them. The UN inspectors destroyed enormous amounts of them. He used them on his own people.
Why Saddam? Because he was a monster that we helped to make. I don't think you can say that of anywhere else in the Middle East. At one point you could have said this about the Shah. How did we help make him? He was the enemy of our enemy, Iran. We played both sides of that war, but in the end gave Saddam what he needed to win. By the time GHW Bush went to war against him, he had one of the largest military forces in the world.
GHW Bush, Cheney, Powell, et al would not go into Iraq to take out Saddam then. The coalition was fragile. Arab nations that took part in pushing him out of Kuwait and protecting his other neighboring states would not participate in such an invasion. GHW Bush was quite public in encouraging the Iraqi people to rise up and rebel against Saddam, and suggested we'd provide support in the effort. They did rise up, no support came, and Saddam massacred them, using WMDs on the Kurds in the North, and he destroyed the livelihood of the people in the South by cutting down their date trees.
Why in 2003? Numerous reasons.
Because a decade+ of sanctions against Iraq were devastating to its people.
He diverted money from oil-for-food to build palaces while the children in his country went without and died.
The sanctions were unpopular with other nations in the world.
Other nations were ready to normalize relations with Iraq. Air France had resumed flights to Iraq, for example.
He used promises of oil deals to buy the favor of European countries and Russia and China if the sanctions would be ended.
We were flying over Iraq to enforce no-fly zones so he wouldn't massacre his own people.
His military routinely fired upon us, we routinely fired back.
The blood of those Iraqis who did rise up against Saddam was partly on our hands.
With him gone, sanctions could be removed, relations normalized, and the profits (in theory) would go toward building the nation instead of building palaces.