This invading king is incredibly stupid. In the absolute best scenario, every other country would turn against him violently and see him as a threat to their existence. No one is going to be like "Oh yeah, you saved them!" They'll be "How were you there so quickly and how did you even know this was happening?" And "If the labyrinth was the problem, why are the monsters invading from outside and not even ones from the labyrinth in the first place?".
Writers tend to have an idiotic, liberal view of "People in power bad" or something like that and portray them as just going along with stuff like this. But, they wouldn't. They would see it as "This could happen to me" and would gang up on the thread, which is this guy and his nation, and eradicate it.
They also wouldn't want to deal with keeping control of the labyrinths and monsters, either, and would be happy to leave it to this small kingdom to deal with.
