Which estate fits this mediating task?

The estate that lives from landed property. Family life is its basis, and the land gives it its living.

Why this one in particular?

Its will rests on itself. It does not depend on others. And it has something in common with the monarch: Nature determines it, through birth and inheritance.

Summary: The estate of landowners fits the task of mediation. Its will rests on itself. And like the monarch, it gets its place from nature.