From Yukihiro's point of view, a little probing would only leave him with a bad taste in his mouth at this point.
Yoshitaka would definitely use the Mitsui Group's influence to harass the Yamaguchis in every way, framing it as a campaign against mob violence or even reviving cold cases.
It would definitely inflict a lot of losses on the Yamaguchis, if not outright deny them a year's worth of income.
Even if they were seething, they wouldn't self-destruct to bring the Mitsuis down, and might e