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Problem being that if they kidnapped Saddam and didn't conquer the whole country they'd create a power vacuum that probably would have been filled by his sons, who were even bigger pricks than he was. So, chances are, it would have made things even worse.
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So we expand the operation then, arrest his sons, and as many of his supporters as possible. If any of them attack, they will be shot. The Americans can set up a temporary government, and new political parties can set themselves up ready for an election.
No need to bomb the holy bajesus out of the place, just need to arrest/shoot up a few nasty types, get Iraq back on track, and get out again.