css is Turing complete, XSL-T is Turing complete, so I don't think Turing completeness is a good measure of if something is a general purpose programming language. I would argue for environmental completeness - does the language have the possibility of accessing everything in the operating system it runs in? If so, it is environmentally complete and usable as a general purpose programming language.
Despite something being a general purpose programming language there are some tasks it may be better at than others. Visual Basic is a general purpose programming language but really you would most often use it for a particular subset of purposes. Elixir it seems is not good for writing a CLI.
I was mostly clarifying what most people I've met believe is a "general-purpose language". I agree with your take on telling it like it is for the practical needs of the commercial programmers / users of a language.
And again, as a guy who loves Elixir, it absolutely is not suited for writing CLI tools. Many would say it can be easily done, the community even has a few really good libraries for it as well, but the BEAM VM startup time absolutely kills its utility for tooling for me.
And, as others also said, Erlang / Elixir simply excel at orchestrating a lot of runtime micro-agents, each with their own small responsibility. And they do this better than any other language I've seen. But, for one-offs / scripts / CLI tools, Golang / Rust are very difficult to dethrone. We could also add Zig / D / V and others, I suppose, but I am not familiar with them.
yeah sorry, I've just got some trauma from people claiming that languages can be used for stuff they can't really be used for just because of Turing completeness.