The one big use case was RabbitMQ in a messaging app, not HFT. I doubt Elixir even with Nx can compete with low-level HFT code. Python DL/ML code libraries are just wrappers around C too. Maybe if BeamAsm and Nx are used Elixir could be used for more numerical or not just distributed applications.
I've programmed in Python and Julia, and when I worked at an engineering (mechanical, entertainment engineering) company, Julia was great for its similarity to Matlab. I am a self-taught engineer, so I did not get pulled into Matlab in college.
Personally, I took to Erlang, so I could write plugins for Wings3D back in the early 2000s, but I never stuck with Erlang, or Wings3D (Blender3D was my choice and I even contributed to have it go opensource way back when). I like Erlang's syntax better for some reason, although Elixir's is beautiful too. I was not a Ruby programmer, and I had delved into Haskell and Prolog, so I think Erlang made more sense to me. I think Elixir has a lot more momentum behind it than Erlang, but at the root it's Erlang, so I think I'll stick with Erlang for BEAM apps. My favorite language is April[1] (APL in Lisp), and given my love of J, would be a better fit for any finance apps I might write. I am trying to convert some of the Lisp code in this book, "Professional Automated Trading: Theory and Practice" to April.
Maybe I'll write some equivalent Elixir code to compare.
[1] https://github.com/phantomics/april