"Carrying a gun gives pilots one more thing to worry about and protect." I strongly disagree. Being armed is one less contingent to be unprepared for. Were I a commercial pilot, no gun, no fly. As a commercial passenger, I won't fly until the pilots are armed.
BTW, to those interested, the FAA used to allow pilots to be armed at their discretion. What happened to this situation was a California commuter airline pilot,
AFTER being fired, immediately boarded one of his airlines planes with his pistol. Pilots were not screened then. After achieving cruise altitude the armed, terminated, still in uniform pilot entered the flight deck and killed the pilot, co-pilot and then himself. The Plane a DH-9 jet, plunged into the earth.
Instead of requiring procedures for the termination of pilots and their access to the flight line after termination, the FAA imposed the firearms ban.