I think you're confusing rigorous processes with rigorous theory. The analogy of steam engines seems appropriate - they were initially built with (sort of) rigo

I think you're confusing rigorous processes with rigorous theory. The analogy of steam engines seems appropriate - they were initially built with (sort of) rigorous processes for metal forming and joining, etc. It wasn't just people tinkering in their backyards. Yet that was done without the theory of thermodynamics. Those rigorous engineers didn't know a Helmholtz free energy from a free energy machine. Once we had thermodynamics, it didn't directly influence how to form metal parts or lubricate pistons, but it did put hard constraints on the possible performance of engines and made it easier to predict how an engine would perform before building it, even if it was outside the range of what had already been tested - eg. jet and rocket engines that required high confidence in predictions of the theory to invest the money needed to develop working models in the middle of wartime scarcity.