This King is similar to Trash from ShieldBro story, started like a corrupted piece of shit, and then learned his mistakes, realized his wrongdoings and in the end directed the country and the people in the right direction, in a way that if he was executed or dismissed at the start of the story it would have pushed humanity to the brink or outright lost.
Of course this king didn't do that much, but deciding to severely punish every noble is a good sign.
Now I don't fully understand the main party discussion, "court adventurer" made MC istantly think of somethign terrible, from the term I think they are thinking adventurers are getting over their head after the hero party achievements and want force themselves into a pseudo royal status?
When this world is crappy is nice that they explained the best minds and strongest guys are absent because the bitch demon queen made them useless, so the ones left "sane" are mostly the leftovers.