The same-day deaths of two aging chief executive officers—industry icons in railroading and banking—show why some investors and governance experts want companies to disclose more about succession plans and the health of their executives.

CSX Corp.'s Hunter Harrison, 73, died Saturday, one day after news of his medical leave pushed the railroad's shares down the most in six years. M&T Bank Corp. said Robert Wilmers passed away "suddenly and unexpectedly" at age 83—just months after the death of his own heir apparent.

These earthly departures underscore the privacy, governance, and legal issues entangled in one fact of shifting demographics: As the U.S. population ages, so too do the chieftains of corporate America. The average age of a CEO has risen 4 percent in the last decade, and there has been at least one health-related change atop Standard & Poor's 500 Index companies in each of the past three years, according to executive recruiter Spencer Stuart.