No one in the airline industry comes close to Virgin America Inc. on a measurement of efficiency called revenue per employee. That’s because baggage delivery, heavy maintenance, reservations, catering and many other jobs aren’t done by employees. Virgin America uses contractors.

“We will outsource every job that we can that is not customer-facing,” David Cush, the airline’s chief executive, told investors last March. In April, he helped sell Virgin America to Alaska Air Group Inc. for $2.6 billion, more than double its value...