Web servers are fast in Elixir because web servers don’t do anything most of the time - most of the time they are just waiting. Either for request data or for database, etc. Elixir/Erlang are excellent at finding things to do when one of the processes doesn’t do anything, which makes them generally fast at web servers.
There’s also a question of algorithms. If you use an algorithm designed with mutable data structures in mind, it will be unavoidably slower when used with immutable data structures - on the other hand, there are some algorithms designed for immutable data structures and different, more specialised structures that can shine in some cases.
Finally, there’s the matter of the VM. BEAM is just a very well implemented and a very efficient machine. The runtime system responsible for IO interaction, scheduling and similar things have been optimised over the years. Yes, it does not have a JIT, but the normal emulator is quite fast compared to other VMs. It’s also one of the few register-based VMs in the wide usage, and register VMs generally tend to be faster than the more popular and simpler stack-based VMs.
