In your mind, what distinguishes a language as "general" or "specific" purpose?
I'd argue the community and focus of the language.
Or, to your point, the historic design considerations that led to the creation of the language in the first place. In the case of BEAM, it was very specific.
What I mean is that, you can write CLIs in Elixir. I have. You can write games in Elixir (others have, I haven't). They come with pros & cons. The Elixir community advances on many of those fronts regularly. I could write a web application in C, but I wouldn't.
I would honestly have a much easier time writing a web app in C than a game in Elixir.