I agree that ability doesn't determine wages. But I would like to qualify your statement about what does determine wages. In a free market, wages are determined by scarcity and demand. However, a free market is a theoretical construction that often fails to model reality. For example, free markets do not include coercion, deception or collusion, all of which are ancient and universal parts of human life.

For example, the $0 pay rate of a field slave is not because nobody wants cotton-picking, or because there are too many people who will pick cotton for free.

Indeed. That's why equating pay to ability is pretty silly.