Because it's in the common interest. The social contract doesn't "exist". It's an abstraction that people have agreed upon, in many forms, because it benefits the whole. What things we codify end up as government regulation. What things we don't are moral obligations.
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>The question is clearly, what moral obligations _should_ they have?
I'm confused.
If moral obligations do not exist as you claim, why should we pretend they should exist?