Wow, the manga literally explained it pretty succintly why they couldn't just simply kill the king and people are still bitching.
Replacing a dead king is not at all a simple matter, especially with what this one is/was involved in.
"There's no way Nobunaga-sama's spirit would follow me to this world."
You fool, you absolute moron. You said the words out loud, thus ensureing that it will happen.
It's less training them to be adventurers and more that he knows they likely wont give up on going out to gather food, so he may as well see to it that they're at least capable of defending themselves should they run into monsters again.
Regardless of your feeling about his dad, guy's 100% in the right about this one. Cain was obsessed with his sister, which is really unhealthy for both of them and also not a good look for the family overall.
Dumb bitch thinks she can come crawling back now that he's gained some fame? Not a chance, especially when his pack of loli daughter/wives learn what she did to him.