Mike Shildt, the rookie manager of the St. Louis Cardinals, can’t help but notice what distinguishes him from many counterparts in opposing dugouts as he makes his first trip around the major-league circuit.

Today’s front offices prefer young, malleable managerial candidates—typically recently retired players for their perceived ability to relate with their charges on a more intimate level than their predecessors. Experience isn’t a prerequisite. In fact, four of the six vacancies this past winter went to men who had never...