You vastly over-rate the ability of the government to plan, prepare for and execute a complex plot which involves training "fake terrorists", planting them on planes and allowing hundreds of witnesses on each plane, dozens of which then report the incident with cellphones, to see said "fake terrorists" in action and to report such to their relatives and friends, and to ensure your "fake terrorists" will happily agree to commit to a suicide attack... and then get a real terrorist organization to take credit for the attacks.*
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And you vastly underestimate the ability of said real terrorist organization to simply tell some guys they'll go to paradise if they kill thousands of heathen, pay for their flight training, and let them simply get on planes and crash them into things.
*Because the easiest way to make people think that an airplane has crashed into a building, causing it to collapse, is to hit a building with an airplane, causing it to collapse. The other option involves building several fake airliners, simultaneously redirecting the real flights to areas unknown, hiring dozens of fake voice actors to supplant the "callers" on each flight, or instead paying each caller millions to fake their own deaths, planting hundreds of millions of dollars of explosives in the World Trade Center, and keeping the tens of thousands of witnesses and support personnel involved in this take completely silent, or paying for the separate disposal of all those bodies.
The best plans are often the simplest ones. Simple plan, get on a plane, hijack it with knives, lock the cabin door, crash it. Finis.