Is the son who recites the Quran better more entitled to lead the prayer than his father in the father's house?

It is authentically reported in the sound Hadith that the Prophet, peace and blessings be upon him, said: "The people are led in prayer by the one among them who is most knowledgeable of the Book of Allah. If they are equal in knowledge of the Qur'an, then by the one who is most knowledgeable of the Sunnah. If they are equal in knowledge of the Sunnah, then by the one who emigrated first. If they are equal in emigration, then by the one who accepted Islam first. And no man should lead another in prayer in his place of authority." Accordingly, the father has more right to lead the prayer in his home than the son, if the father is suitable for leading the prayer, even if the son is more knowledgeable and a better reciter than him. Nevertheless, there is no harm if a man leads his father in prayer in his home if it is with the father's permission.