[Scarblac]

And if you don't store the answer in some kind of state, it's lost and computing the pure function was useless.

[HelloNurse]

In typical functional languages state is managed so that it doesn't hurt, not completely absent.

For example, a REPL keeps state in the messages it prints to the terminal and this state isn't visible in the pure function definitions and expression the program is concerned with.

[Life_exe]

You don't have to throw away the result. That's what the State Monads are for. Immutable State is Ok. Memoization is Ok.