Erlang → scalable real-time systems, eg telecoms
(and that being said, you can also use Erlang libraries in Elixir, so there’s a path for incremental adoption)
Or at least that was the case some year ago. Haven't checked lately. I know there are ongoing efforts towards convergence.
Neither option allows you to use Phoenix without writing Elixir code, though. But since you’re integrating an Elixir lib, writing at least some glue code doesn’t seem like a big deal?
(I’ve got to say that I’m not proficient at all neither in Erlang nor in Elixir – I’ve played around with both, but nothing serious.)