Last I checked the US Constitution gave the federal government the power to regulate interstate commerce. While it doesn't say anything specifically about a power to regulate airplanes and aerial navigation (the airplane wasn't invented till 114 years after the Constitution came into effect in 1789), it very specifically gives Congress the power to legislate with respect to navigable waters.
Any plane with enough fuel on board to allow it to overfly the airspace of another state is potentially a hazard to people on the ground in that states. According to some of the engineering experts interviewed after 9/11, the force of the explosions caused by the 767s that crashed into the WTC were equivalent to a 1-2 kiloton explosion. That's as powerful as a tactical nuclear weapon. To say that the federal government should have no power to regulate such a potential hazard is ridiculous.
If states want to allow illegal aliens to have drivers licenses, I don't care, but I think other states ought to be allowed to not recognize drivers licenses from states that issue them to illegal immigrants. The Congress under the full faith and credit clause can write legislation regulating how official acts of states can or must be treated by other states. The federal government is well within its authority to ban the use of substandard state issued identification documents for boarding aircraft.
See post numbers 62 and 118.