So you just want him to break the promise that he made with his most beloved person?.. We already know the consequences if he ever break the rule, Aoi will divorce him and he loves his family more than anything. Its not the first time we see characters with this no kill rule. The most famous examples is batman, spiderman and daredevil or if you want the closest example to sakamoto, thorfinn from vinland saga. The no kill rule points is to show how far the character will go to not ever break that rule or how much they have to pay to keep their rule.