If you want to ackshually, both fiber and copper are empty pipes that can carry any layer 2 protocol, and are not inherently Ethernet. They only become Ethernet cables when they're connected to terminals that pass that protocol through them.
Unless we're defining some networking standard, "Ethernet cable" is a perfectly acceptable term. Everyone will understand what is meant. The added specificity you're asking for doesn't improve the quality of communication.
That's why I added base-*R/base-T.
And particularly for 10GE the heat and power problems are due to the copper transceiver DSPs.
And people nerdy enough to run 10GE at home might well run fibre.
So, no, the specifity is needed and useful.