edit: https://fsharpforfunandprofit.com/ is a very nice introduction to F# and all the things it can do.
Or if you just want to learn it, you can run it in your browser here: https://try.fsharp.org/
The original "wouldn't it be better if we just passed data around through simple composable functions" kinda won, you have first-class anonymous functions with support for closures in most languages today in use :-)
I think the next pitch is along the lines of "We can solve the evil of mutable state making your app hard to debug/test" and i.m.o. that took over a bit as well, i.e. with frontend we usually have state in one tree sitting somewhere and what we display is just a function from state to our html.
And I have seen the state being represented as a fold/reduce over events in the application.
So the pitch i.m.o. is along the lines "Hey, we converged on the idea that functional programming is good, why not use language that has good support for it" :D
Learning Haskell was probably the single best thing I've done with regards to becoming a better programmer even I've never really written much Haskell since then
Do you really need types? I did work in Clojure and I think having good support for immutable data-structures got me 80% of the benefits of functional programming.
Similarily, maybe you are sold on actors and message-passing and Erlang/Elixir is proven there :)
Or you would like types, but are not sure about the whole separation of IO from pure functions in type system, you could try Ocaml (or its Javscript-looking reskin Reasonml). Like, you don't get type-classes, but polymorphic variants are nice and there is this interesting module system.
Or, if you really want to encode your domain in types and then maybe even use the type-system to solve your programming for you, maybe try Idris? Like I have been meaning to go through 'Type-Driven Development with Idris' one day :)
But maybe Ocaml is too little and Idris is too much and Haskell sits in the nice middle ground you like :-)