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Do you think this way because of scale? Because the regime split was a big event, and a single human deciding to take a piece is small? Is Jim Nobody really insignificant as you suggest? Surely no more or less significant than someone who left their individual handprint on a cave, or who was buried under lava?
History is made of Nobody's.
I agree that we shouldn't just keep history behind glass. But that doesn't mean I support what amounts to arbitrarily damaging it for any old reason. 
The destruction of the Berlin wall is an intricate part of its history. The wall represented the split between east and west Germany, and the brutal repression of the communist regime. Tearing it down was the history. The same can't be said for people taking home souvenir chunks of historical artifacts. The relevant history of these things is often thousands of years old. When you visit the pyramids, what part of their history is more relevant: their construction and history concerning the society that built them, or Jim Nobody breaking some off because it's a cool souvenir?