Alright, let's all take a deep breath here. No one is meaning to attack anyone; things just got a little spirited.
I think the main disagreement with your theory, Reader, is that you're not accounting for the fact that each magic system has a focus: metal for Allomancy, color for Awakening, etc. Yes, the Tears and atium are both manifestations of Shards, but they also take forms that can be used by their respective magic systems. This should tell us something about how the magic works: namely, that even manifestations of a Shard need to take a certain form for it to be usable in magic. If an Allomancer got their hands on the Tears somehow, and ate them, they wouldn't be able to do anything, because their body wouldn't recognize a non-metallic object as a burnable substance.
Make sense?