A) You can't kill dragons until you learn you are dragonborn, similar to how you can't find Oblivion gates until a specific part of the main quest. (Lame idea)
B(friggen sunglasses emote)) You can still kill dragons, but doing it without Dragonshouts is much harder. Any rewards from killing dragons are still given, you just can't see them, use them, or know they are there until after that point in the Main Quest (imo better idea)