As CVS Health's new CEO David Joyner steps into the top job after Karen Lynch's quick departure on Friday, Wall Street analysts and some investors are questioning whether he has the right experience to turn around the Aetna health insurance business as it struggles with high medical costs.

The industry-wide rise in health coverage costs makes the company's Aetna unit the new leader's most difficult problem.

That has been the existential question for CVS Health for six years, since its $70 billion acquisition of the massive insurer Aetna. The biggest pharmacy chain in the U.S. had already been moving beyond retail since its 2007 deal for pharmacy benefit manager Caremark.