I wonder why the king ask hero kill this immortal king? What sin this girl do? Or maybe, the king want to end this immortal king suffering.
If the king doesn't summon a hero, the immortal king will sooner or later get bored and go to the city, where people will learn that she's not as horrible as the king made her out to be and thus not a good cause for the "taxes to defeat the imoortal king" project.
(Also, being an actual immortal, she might have some dirt on the gods, and/or attract worship through being immortal)
So basically the kingdom sends the heroes off as distractions, to protect the status quo.