You're making the assumption that the only reason labor statistics would be useful is if employment is subject complete to supply and demand.
Consider the possibility that labor statistics could be useful simply because they are an aspect of the health of the economy, and it doesn't necessarily matter if they are a result of supply and demand, or has a more complex causality.
Trying to reduce labor to supply and demand only makes things very nice for theoretical considerations, but it doesn't force reality to match theory. Supply and Demand is the same thing as a spherical cow in physics. A useful simplification sometimes, but if you take it literally, you're going to go wrong.
Making assertions about the labor market based solely on an analysis of supply and demand is not useful at all unless your goal is to argue ideology and not reality.
If what you say is true, and they aren't strongly correlated with supply and demand and the health of the economy, then why do we even report labor statistics?