What is the legal religious proof for the impermissibility of the son of fornication leading people in prayer?

The jurists have agreed on the validity of prayer behind the son of zina (fornication/adultery), but they differed on the permissibility of his imamate (leading prayer). The majority of scholars held it to be disliked if someone else is available or if he is a transgressor. However, the Hanbalis maintained that it is not disliked if his religiosity is sound, based on the Prophet's ﷺ saying: "The one who is most proficient in reciting the Book of Allah should lead the people in prayer," and Allah's Almighty sayings: "And no bearer of burdens will bear the burden of another," and "Indeed, the most noble of you in the sight of Allah is the most righteous of you." The most preponderant view is that it is not disliked. Nevertheless, if his leading the prayer causes disunity or harm, then someone else should lead them in prayer.