Ethically speaking, Baiyi was literally taking full advantage of the situation by discussing the terms of the deal with the Duke at a time when the noble was mentally and physically exhausted. This was not how Baiyi usually acted, but this family was really too abhorrent for him to deal with. Thus, he ditched the neutrality of an outsider long ago, no longer interested in advising or reasoning with them.
From the words of the Duchess herself, it seemed that the Duke actually had the chance and the power to put a stop to this family's tragedy before it deteriorated into such a dire state. Instead, he chose to close his eyes to that and stifle any trouble that occurred in the household, eventually leading to such a tragic outcome.