Yea, this is like the early railroads making steel cheaper via cheaper transport of bulk ore/coal, that made cheaper railroads, that then ship more products made of steel to larger markets opened by the extended rail networks, etc.

This happened with tin all the way back in the Bronze Age, where a lot of it was shipped as ingots from industrial-scale mines / smelters in Cornwall all the way to the Mediterranean empires to mix with copper to make Bronze.

A cog-based auto-catalytic wood industry is super interesting.