How long would the pilots keep the door sealed with the flight attendants and/or passengers being killed and/or tortured on the other side to induce them to open up? That is apparently what happened on at least one of the planes Tuesday.
It is trivial to design a door that cannot be opened while airborne. An interlock that requires the landing gear to be down and sensors to sense that the gear is supporting the weight of the aircraft would work nicely. Something similar is employed on some military aircraft to ensure weapons cannot be launched from the ground by accident. Just works in the opposite way.
Another thing you might wish to consider is to soundproof the bulkheed separating the cockpit and passenger compartment and to ensure that no direct communications can happen between cockpit and the passenger compartment. The aircrew can only communicate through a ground station. This shifts the burden to the ground station but procedures denying this information to the cockpit are much more apt to be followed there.
BTW, in order for this to work, we needed an example such as this to happen. In the past, we found that violence and loss of life could be prevented by giving the hijackers what they wanted, usually tranport to another location, and they would release the passengers. Not any more.
This will be very tough on the first set of passengers. Someone will want to test it.