Given how much old cabling, especially old Cat cabling, currently simply gets dumped due to the costs of trying to reclaim the copper, a substantial shortage might change the economics.
Additionally, it would seem an increase in the cost of copper may also change the economics of running Catn verses fibre: why install Cat8 when you could use fibre?
This would have a (potentially small) impact on the demand for copper, reducing that shortfall.
Aside: perhaps the time is right to replicate the 1980s events in the Ethernet world, where a proposal for a new IEEE802.n working group to focus on LAN over twisted-pair was changed into a new subgroup under 802.3 CSMA/CD aka Ethernet. Hence with fibre perhaps we should say take Single Mode (OS2) fibre and LC UPC Simplex connectors and brand it Cat9.