While a carthagenet tag would be valid to create, the reason you don't see one is that the community is learning how to better scope the context of testnet related issues.
As described in the documentation, every new successful protocol amendment we effectively have a new primary testnet which mostly mirrors the new mainnet protocol (that today would be carthagenet). Some short time after that a new proposal will appear and we will launch a testnet for that which is our secondary testnet or "proposal testnet".
Once us mods get around to cleaning up the tags again, I am going to propose we use 2 tags consistently: testnet-main and testnet-proposal. But the ensuing discussion around that will help determine if this makes sense or if the more specific use of tags which change every few months continues to be a better a approach.
Note that to make it even more complicated, the testnets im referring to are the long lasting testnets. There are also various shorter living testnets which people might have questions about which are entirely different. And then of course the newer experimental testnet known as labnet is in its early days.
A testnet taxonomy so that we are able to consistently identify, locate, and communicate about testnets would be helpful; not just for stackexchange tagging but across the ecosystem tooling and discussions.
