Ms. Saracini said the secondary doors were a small price to pay to prevent another terrorist attack.
In 2007, Northwest Airlines, which has since merged with Delta, installed secondary doors on some flights but decided against installing them on all the planes in its fleet.
An F.A.A. report in 2011 concluded that of all the security measures — including human barriers and galley carts placed before the doors — the secondary doors were the most "cost-effective, efficient and safest way to protect the cockpit".
"Installing a secondary barrier door to the cockpit of our aircraft is not in the current plans for our fleet," said Michelle Agnew, a spokeswoman for Southwest Airlines.
Delta Air Lines did not respond to questions about the secondary security doors.
Most airlines contacted said they did not have the secondary barrier doors and had no plans to install them.
A spokeswoman for the F.A.A. said the agency would review any legislation on the secondary security doors but would not require them unless directed to do so.
The Federal Aviation Administration and the T.S.A., agencies with oversight of airline security, have acknowledged that the secondary security doors provide additional safety.
Ellen Saracini, whose husband, Victor, was the captain on the hijacked United Flight 175, which crashed into the World Trade Center's South Tower, said she learned in August that United had begun removing the secondary security doors from newer planes.
The secondary school next door, the only one in 25,000-strong Katine sub-county, is an aspiration too far for most children.
