While I don't believe that the government really did it, the gain is rather obvious. By planning an attack against yourself than a foreign combatant would willingly accept claim for, you justify war. Al Qaeda would gladly take responsibility for an attack against the United States. Why would the government want to justify war? Most likely, oil. People talk about the war on oil a lot, but it's rarely understood. In all likelihood, you don't have American companies like Exxon Mobil going into heated combat zones drilling oil. What you do have is the possibility of a new democratic, American-loving, Western-esque regime. Such a regime would probably be more willing to allow American oil companies to come drill.
If that is true, then why have oil imports from Iraq only decreased since the invasion, and why were the hijackers depicted as Saudis and not Iraqi, and why did we invade Afghanistan first? Please answer these questions, because your story isn't making any sense. Why did a whole new conspiracy with WMDs have to be constructed when the hijackers could have simply been depicted as Iraqi agents?