Yes they have. Despite the rhetoric from the enlightenment. Significant portions of the population in the West maintain a fascination with those who are considered ‘above them’ in the social/economic hierarchy of human society. And the office of the President is considered the closest thing America has to Royalty.

So the office is subject to close scrutiny. And a President essentially disappearing out of the blue without a reason or statement of any kind. Especially one as famous for loving the camera and public appearances as Trump. Is liable to provoke speculation domestically and cause concerns among foreign leaders internationally. Especially given he’s been banging the drum and rattling sabers of late.

A formal statement however vague it might be. Does a bit in disarming the tension and rampant speculation among foreign leaders. As well as the rampant speculation domestically.

Ala rumors of him being bundled off to a Nuclear Shelter quickly or something else that might provoke concern or panic are nipped in the bud. And instead the speculation will instead turn to more typical Washington Drama. Health Concerns, Family issues etc.