It makes no sense to me to use Elixir without running on the BEAM. Absolutely zero. You lose OTP, for one thing, which means that the entire programming paradigm goes out the window.
The BEAM also provides a runtime, but that runtime can be implemented using other strategies. It essentially provides a M:N green threading abstraction (processes), with a specific set of semantics around how those communicate (messages) and how failure is handled (links/monitors/etc). Firefly provides a runtime that aims to be equivalent to that of the BEAM from the perspective of the developer, the only difference is in how that is done behind the scenes, what is produced by the compiler, and what restrictions we impose that the BEAM doesn't (namely no hot code loading, at least for the forseeable future).
I'm not sure where you got the idea that Firefly throws away OTP, or tries to implement Erlang with different semantics, because that is explicitly _not_ the goal.
Lots of people have written alternatives to BEAM. The only problem they run into is that BEAM is very good, and would be tough to beat. I was an admirer of Erlang on Xen: https://github.com/cloudozer/ling
I agree that Elixir without OTP becomes much less useful, but there could be some changes to the language to enable in-process state changes so that you wouldn't be limited to a single process and the immutability restrictions that would make that very difficult to do anything useful with. I'm sure they thought of this problem and have a solution in some form.