It would be great if there was a checkbox in the field settings to make the field hidden if there is no content
(Note: would not be an option if the field is "required")
Basic idea is to limit what is displayed for an item view by wrapping the output in a conditional check.
If there is content for the field, then the front end view should display that field; other wise skip that output.
example old code for a link text field (modified to actually be a link) for a front end view