By JANE S. SHAW

When North Carolina’s new governor, Pat McCrory, was interviewed last week on the syndicated radio show hosted by former U.S. Education Secretary William J. Bennett, the talk naturally turned to education. According to some listeners—or those who heard about the interview in the media echo chamber—Gov. McCrory committed a major error.

No, he actually just stated an uncomfortable truth. Gov. McCrory, a former mayor of Charlotte, said he is concerned that many college graduates can’t get decent jobs. The problem, he suggested, might be that many academic disciplines have no real practical applications.

Referring specifically to North Carolina’s 16-campus state university system, Mr. McCrory wondered if state funding incentives should encourage areas of study that align with the job market. Other disciplines, such as gender studies, Mr. McCrory said, might be subsidized less. The funding formula, he said perhaps a bit indelicately, should not be based on the number of “butts in seats, but how many of those butts can get jobs.”

The education establishment immediately went bonkers. The pundits piled on. But Mr. McCrory raised a legitimate concern. And the solution he proposed, sketchy as it is at this stage, is not a bad one.

The truth is: Elite universities, such as the University of North Carolina at Chapel Hill, are doing a disservice when they lead students into majors with few, if any, job prospects. Stating such truths doesn’t mean you’re antagonistic to the liberal arts.

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Yet some, always eager for a fight, misconstrued the governor’s comments as a call for abolishing liberal-arts education in favor of vocational training. UNC-Chapel Hill geography professor Altha Cravey said the governor “was not elected to decide what has intellectual value and what does not.” Sociology professor Andrew Perrin said that the governor’s comments reflected “a fundamental misunderstanding” of higher education.

Instead of treating Mr. McCrory’s statements as an attack on liberal arts—and thus missing his point—the education community might instead pause to consider the validity of his criticism. They could even acknowledge the possibility that many taxpayers, perhaps a majority, share his views.

The governor may have understated the case. Many liberal-arts graduates, even from the best schools, aren’t getting jobs in large part because they didn’t learn much in school. They can’t write or speak well or intelligently analyze what they read.

The National Association of Educational Progress indicates that literary proficiency among adults with “some” college is declining. Richard Arum and Josipa Roksa, authors of the 2011 book “Academically Adrift: Limited Learning on College Campuses,” found that 36% of college students made no discernible progress in the ability to think and analyze critically after four years in school.

For many students, college is a smorgasbord of easy courses chosen for their lack of academic rigor. There is no serious “core curriculum.” Students spend limited time studying. Faculty and administrators make matters worse by allowing students to fill up their time with courses like UNC-Chapel Hill’s “Dogs and People: From Prehistory to the Urbanized Future” and “Music in Motion: American Popular Music and Dance.” When students can get a minor in “Social and Economic Justice” without ever taking a course in the economics department, it’s hardly surprising that businesses aren’t lining up to hire them.

As it happens, North Carolina’s Pat McCrory is not alone. Former Indiana Gov. Mitch Daniels, who recently took over the helm of Purdue University, has suggested much the same. In an open letter to the Purdue community, Mr. Daniels cited a long list of challenges facing universities, including complaints that “rigor has weakened.”

To meet such challenges, he said, those in higher education can’t afford to look the other way. “We would fail our duty of stewardship either to ignore the danger signs all around us, or to indulge in denial and the hubris that says that we are somehow uniquely superb and immune.”

U.S. colleges and universities aren’t “uniquely superb,” nor should they be immune from criticism. This is the time for humility and introspection, not circling the wagons.

Ms. Shaw is president of the John William Pope Center for Higher Education Policy in Raleigh, N.C.