Why not just install a cockpit door that is impenetrable?
Because it is impossible. Aircraft manufacturers have clearly stated that even the strongest possible door will not stop determined attackers. Serious technical issues dealing with a loss of cabin pressure and practical issues concerning incapacitation or seizure of a pilot put limits on how strong the door can be. A much stronger cockpit door than those that now exist is clearly required, but we cannot rely on any cockpit door to deter or prevent a cockpit takeover from a team of terrorists. A significantly strengthened door will slow attackers down, giving an armed cockpit crew warning and preparation time to defend their airplane.
