Would yi yin accept the notion that there can be a distinction between rulers private morality and public policies?

No, Yi Yin would not accept a distinction between a ruler's private morality and public policies. According to the Mandate of Heaven, those rulers who failed did so because they lost the endorsement of Heaven, and this would happen if they ruled without honor. Yi Yin felt that a ruler was tied, then, to who he was: how he ruled was a direct representation of his morality. He specifically referred to former kings of Xia to supplant this point of view, claiming that their rule was successful because they ruled in a virtuous way. So to lose the mandate would be to lose power itself.

Dictatorship is the answer you are looking for