Kaito did not sleep at all through the entire night after leaving the Crown. His altercation with the members of the yakuza was not the cause of his sleepless night. He realised that he could not leave things as they were with the Shadow Brotherhood.
If he let go of the situation without addressing the core problems, a disaster would probably find him and Akira.
For example, his lack of attention to the outcome of the prisoners he locked up in the Ground had resulted in an attack at his home. If he was not vigilant and his training had not improved, the ambush might have caused more trouble.
He could not be certain about the fate of the rest of the other two prisoners. Those two were the most dangerous because they always worked as a team. If they tried to harm Akira, the outcome might be highly dangerous.