That's wrong. You say it had the required elements. The required elements, as we were told, were that:
1. Iraq was involved with 9/11;
2. Al Qaeda was involved with Iraq in some way;
3. Iraq had weapons of mass destruction.
That's it. Those were the reasons given, and no others. It turned out that all three reasons were WRONG. If you remember, hitting Iraq was discussed by Rumsfeld almost immediately after 9/11, per Richard Clarke (the White House terrorism czar), before they even knew who hit us. One thing Clarke knew: Al Qaeda did it, and Iraq had nothing to do with it.
The war was very destructive for the country, leading to a Great Recession ultimately, loss of trust in us by other countries around the world, cost of billions of dollars we are still paying for, and not shutting down Al Qaeda in Afghanistan as effectively as possible because of the diversion of Iraq (costing us American lives and tons of money over a decade).
Finally...one of the most important costs (and the White House was warned about this): THE IRAQ WAR IS WHAT HAS ENABLED IRAN AND NORTH KOREA TO FURTHER THEIR NUCLEAR PROGRAMS and establish their countries more in the world.
Our leaders outright and intentionally lied to us. Wolf testified to that before Congress (remember the hearings?).
The real reasons for going to war: Bush wanted to get back at Hussein because his dad hadn't finished him off; and oil. (Cheney's company Halliburton walked away with billions from the Iraq War, due to no bid contracts, payrolls for fake jobs, and outright stealing of buckets of cash.) Remember how the U.S. did NOT protect the museum (some of the oldest artifacts in teh world were there, since Iraq is where the FIRST CITY IN THE WORLD was located), but DID protect the oil rigs.