There is also Article 20, saying in part: "The Federal Republic of Germany is a democratic and social federal state.
So the social obligation of property isn't a fluke, but more a consequence of this provision.
The "social" is really important here and it is being interpreted as a real duty of the state to achieve social welfare. And it is so central to our constitution that it is protected by the "eternity clause" in Article 79:
"Amendments to this Basic Law affecting the division of the Federation into Länder, their participation on principle in the legislative process, or the principles laid down in Articles 1 and 20 shall be inadmissible."
And of course, changes like this would be likely to happen in political environments that don't care about these things.
(Teleological interpretation)
What I mean is, I think history has shown that the "best" definition of property (as in, which one has the best outcomes for society) is one that's "mostly private". Full Communism clearly doesn't work very well, but an absolutely inviolate right to private property carries all kinds of problems too, so instead most countries have settled on a flexible definition where there is private property with an enumerated set of restrictions and limitations (which a hardcore Lockean can't do, because to them property is absolute). The sentence in the constitution seems like a reminder of this when it comes time for a constitutional judge to evaluate a particular law, which I think is right - a constitution can't cover every possible situation, it should be a set of guidelines for entering unfamiliar territory.