Part of where the disconnect for us is the word "whiff", and I blame DM's for narrating misses this way (including me). The dude had a 12 AC until he put on fullplate. My 15 attack did not whiff. It went *KLUNK*. In my mental schema, this opens up a realm of possible narrative outcomes.
Yep. An analogy from another board I'll borrow is that a hit in D&D is akin to a hit in baseball. It has nothing to do with contact being made it has everything to do with an exposed area being exploited. GWF is akin to hitting a line drive that a fielder (re: armor, parry, etc.) doesn't field cleanly. You don't get credit for a hit, but you're still partially successful (ie: you get on base or you do a little damage).