All of those can be structured as processes. All of those can be independently fault tolerant. All of those can be inspected while they are running...in production. Seriously, for HA APIs or web apps it feels like a no brainer.
I just wouldn't us it for things that are CPU bound, like image processing for example. Try implementing something that is a bottleneck in your system in elixir and then throw some data at it and see how it performs.
Elixir + Phoenix is a real treat for web app devs.