Why do Sunnis not affirm the Wilayah (guardianship/leadership) of Ali ibn Abi Talib and his sons as Imams?

The People of Sunnah are unanimous about the wilayah (guardianship/sainthood) of Ali ibn Abi Talib, may Allah be pleased with him, considering him a wali (friend/saint) of Allah, because he was among the earliest converts to Islam, and the Prophet, peace and blessings be upon him, bore witness to this for him.

As for his wilayah in the sense of his greater right to the succession of the Prophet, peace and blessings be upon him, in religious and worldly matters, this is not accepted, due to their consensus on preferring Abu Bakr and Umar over him and their greater right to the Caliphate, and he pledged allegiance to both of them.

As for the wilayah for him and his descendants in the sense of infallibility and the exclusive right to religious authority, this is rejected, because the basis of preference in Islam is piety and faith, not lineage.

The doctrine of the People of Sunnah and Community is that no one is infallible except the prophets, and their infallibility pertains to conveying revelation. They are infallible regarding major sins but not minor ones. The Household of the Prophet, like other human beings, are not infallible, and every human being errs.