I think that this is only part of the story. It isn't only that we didn't possess the technology to mass-produce these things, we also lacked the need to produc

I think that this is only part of the story. It isn't only that we didn't possess the technology to mass-produce these things, we also lacked the need to produce these things at all, let alone in mass-quantities. The need for a chain that is used to transfer energy between two gears, like a bicycle chain, would only be apparent to you if you had a regular source of energy, like say an electric motor or internal combustion engine. After realizing that these things could be used to turn motors at unprecedented speeds, you would naturally look for ways to more efficiently transfer energy between the motor and a receiving point to harness the energy for something useful. Then you would design a system of gears and chains.