I never noticed until I started trying to weatherstrip my front door, but it appears the door once had a taper to it. That is, the width of the interior face of the door (hinge side to latch side) is about 1/8" wider than the exterior face. Unfortunately, over the years, people have tried trimming the door unevenly to compensate for movement of the doorway, and it's hard to tell exactly what the original profile was. It occurred to me that such a taper would serve to make a tighter fit when the door is closed. Am I way off base?

You are correct. Most doors are tapered on the latch side.