Increasing Armor Class: Why make attack rolls at all if the game is designed for you to hit at least seven of the ten times you roll the dice? The joy of a success is only satisfying if there’s a realistic chance of missing.
I would have gone the other way and just removed the two-hit check altogether. Missing isn't fun. Missing makes no progress. Get rid of it.
I don't think this would seriously solve the problems I have with DND. The adventuring day model is a huge source of problems. The inability to reason about much of the world (I see a knight on the road. How many hit points does he have? 10? 20? 200? This information would inform tactics but is not provided). Many other problems I don't feel like enumerating.