Another thing to think about is that exceptions make our code impure. [...] A referentially-transparent function will always give the same result for a given input. But we can’t say this about functions that throw exceptions. At any moment, they might throw an exception instead of returning a value.

That’s just incorrect. If it’s a pure function, it would always throw exactly the same exception given the same input. It would still be referentially transparent.

Sure, it’s a pure function with two exit paths, which is more of a hassle and possibly more error-prone to deal with. But it can still be pure, so you can still get the benefits of pure (dynamically-typed) functional programming.