There are several key distinctions about Elixir vs the other languages you mentioned. These are things that are basically not going to happen in Ruby, Python, Go, Javascript, or etc.:
1) You get the benefits of Erlang/OTP as others have mentioned in their replies.
2) You also get the amazing macro capabilities (runtime code execution and runtime code generation, a la LISP) that Elixir brings to the table. Many of the language features of Elixir are written in macros in Elixir. The source to both Elixir and Phoenix are quite elegant and educational to browse, and demonstrate this runtime code generation aspect very well. It's straightforward in Elixir to introspect code, represent that code as data structures, manipulate those data structures, then generate or execute that code, as you can in LISP.
3) Immuatable data and functional style leads to better code in lots of ways. This is what really makes the benefits of OTP possible (updating the code without restarting the servers, easily migrating state between servers, and so on). But it also makes certain kinds of situations easier to understand and fix, since all state in the system can be expressed as parameters to functions.
Erlang provides great abstractions for building fault-tolerant, scalable, distributed, soft real-time systems. That's not to say you can't do it with Erlang, but Erlang does give some simple, yet very powerful tools for making developer's life easier.
Without Erlang you have to work harder to get similar effects. Again, it's not impossible but there's more burden on developers because the runtime provides less guarantees. I elaborated a bit on the topic in the promo interview for my book (http://www.infoq.com/articles/elixir-in-action-erlang-review).
I switched to Elixir and Phoenix last year and got the core of my app working.
It's funny though - the core is easier. But many freebies from Rails aren't there yet. So I still don't have password recovery emails or confirmation emails on signup done yet :)
Then you must create the login page.
Then the controller for authenticating. And then you need to ensure that the flow works with a test.
Then you need the email that actually activates the account, with the activation hash. So now you're setting up a mailer system, which Phoenix does not have by default.
Then people will want to recover passwords. So you need to write the logic for that. Oh, and the controllers and views. And routes.
And of course, you need to hash the password using some kind of encryption. Excrypt, comeonin, what have you. Choices choices choices.
You'll need a plug to act as the bouncer for your routes too, so nobody gets in where they shouldn't. So you'll have to write that.
You have to end-to-end test this, of course. And probably, if your business depends on it, get a couple other people to review the security of your system.
Simple. And takes a long time.
HTTP is pretty simple, but we use frameworks. SQL is pretty simple too, but we use Ecto now.
It's simple in its pieces, but I really don't wanna do all that work on every app. I'm lazy.
i'm not aware of anyone running an erlang or elixir repl over http but it would be an interesting project