I don't think this logic applies to well to modern civilisation.
Your analogy supposes that their is a semblance of government in nature. If it was a realistic case, the wolves would take what they want, regardless of the sheep. Nature is based on survival, not government.
I support democracy, but it's not a completely direct democracy.
America is a representative democracy. People vote for whom they want represent their county, or constituency or whatever, for whom they want to represent them. Not all people agree. And it's not perfect. Direct democracy means that everything is funnelled to one power, and everyone gets one representative, which practically doesn't work. Especially when America is a big country, with states which govern differently from each other regarding law and tax.
And Republic falls on a pretty broad definition. The USSR was a republic, but it wasn't really democratic, especially with a one-party system. And look how that turned out.