Since the dawn of the NFL, head coaches and general managers have been calling top college quarterback prospects into conference rooms to pepper them with rudimentary questions: how to attack a certain defense, for instance, or what to do when a play breaks down. The answers were sometimes dull and sometimes brilliant, but there were always answers.

This year, according to separate interviews with dozens of NFL coaches and executives, something disturbing happened in these pre-draft quiz sessions. When asked the same basic...