At best, there are degrees of concern a president should have for individuals captured overseas.

They may be in dangerous lines of work, like reporters or humanitarian workers in war-torn areas.  Or they may be students or business persons in lawless regimes.  Or they may be doofuses who invite the trouble they stumble into.  The kid in North Korea who stole the poster or the "hikers" who were taking a walk on the Iraq-Iran border several years ago come to mind.

The president, whether it be a grown-up like Obama or a man-child like Trump, can't be hamstrung in his foreign relations by considerations of such individuals.  That is one of the things a fully staffed State Department can do for him.