Nope. No such system.

You may be confusing the envelope protection with the ability to hit the planet. You can not exceed the pitch limits so no, you can not dive a FBW Airbus at 60 degrees... limits are 30deg nose up, 15deg nose down, 67deg bank angle.. in NORMAL Law. You would have to fail some systems to go outside the normal envelope to get to Alternate or Direct Law control and to do that requires knowledge that is beyond many of the guys who routinely fly the 'Bus.

And the main thing was they had trained on Boeings and wanted a big airplane (mass) with lots of fuel (heat potential) to create the bomb to destroy the Towers.