Why did Itachi killed entire Uchiha clan, he could hv just killed his father and main leaders to stop the coup d'etat, like atleast spare the children

Some of you may say that hiruzen was a asshole (fax) but Itachi has his own intelligence as well you know , he could hv just killed all the main leaders and maybe hope that future hokage will try to bring peace,

Like killing entire clan just feels stupid, atleast spare the children

Even if the point was to eliminate all Uchiha then what about those who were out of lead village at the time ?

But in my knowledge there are cases in real life where countries where about to split but didn't due to proper power distribution imposed by government like country Belgium , i mean in real life we don't hv overpowered eye hacks but still Naruto universe has intelligent enough people that could hv divided the power well

Is this answered in manga or something?