"In other words, your labour is worth nothing unless you produce something other people want."

Karl Marx actually agreed with you there, and wrote about it at length. His concept of "reification" is pretty close to how we describe fiat.

In the real world, the labour theory of value and the market theory of value are tightly coupled, especially for goods and services not easily stockpiled nor transported.

The value estimates only diverge significantly where and when people are not rational economic actors. Market value is not easily predicted under those conditions, either.