> Unpredictable exception-throwing only happens if the work being done by your function isn't pure, i.e. it depends on something other than the function parameters.

This isn't true. The canonical example is trying to grab the first element of an empty list. You either check and catch the error or eat the exceptional behavior, but some pure functions are just partial and aren't defined for all inputs.

(Whether or not they throw a catch-able exception depends on language/implementation and is really not relevant to my point.)