It seems my confusion was that 'a' represents a generic in Haskell. Since the parameter is generic the function can't perform any type-specific operations on the value (e.g., creation or modification), and since it doesn't accept a function to apply to the values in the list, the only thing it can do is return one of the values it was given.

Yes, exactly. There's no way to construct a value of an arbitrary type -- outside of non-termination[1] (which doesn't really produce any values) or abuses of unsafeXXX functions. I think I perhaps should have been more explicit in my example. It could also have been specified as

   f: forall a . [a] -> a

which would make it more explicit that the function has to work for any given 'a'.

[1] ... which I think I should have actually specified. The function type given does not preclude non-termination in Haskell. (You can specify such things in Idris/Coq/Agda, but the effort of implementing f can be much higher if you have to prove totality.)

If said a implements the Num typeclass (can kind of think of it like an interface) then you can perform Num specific operations such as adding/subtracting or averaging.