Erlang was developed to solve problems that are quite common in Web Development like concurrency, high availability and so on. I see Elixir basically as a user-friendlier version of Erlang with some added goodies. So I think it makes perfect sense for it to be popular among the Web crowd.
It definitely has it's own problems(ease of deployment, package maturity, imo). But if your problem involves networks I think Elixir is at the very least worth having a look at.
Deploying Elixir is extremely easy with Distillery, I think.