You're wrong in your broad, abstract argument in a really obvious and shallow way:
It doesn't explain why the predominant strategy of life at all scales is mutualism and synergy between scales and kinds of life.
In no particular order, your "technical" argument fails to explain: eukaryotic structure, multicellular life, the interplay of fungii and roots, forests (which are more than adjacent trees), and really just about anything we see in the natural world. (Ed: I've thought of another 5 or 6 examples if you want to protest those -- mutualism is pretty easy to pick out in nature.)
And that's because you've failed to account for localized regions of stability able to ratchet themselves to greater and geater levels of stability -- and these metastable systems are the model we see on every scale of existence. Life does this as well, which means that we always see stable collaborations outpace competition (and unfairness) on an asymptotic scale. You literally failed to account for how life does work in your argument.
So I still don't believe you're advancing either a genuine observation (ie, it doesn't match fact to say it's unfair in general) or a principled theory (ie, it doesn't actually seem an internally consistent model -- at least, if you believe in physics).
I think you're trying to build a post-hoc justification for the human system being as it is.