Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) said: When prayer was offered for the Messenger of Allah (peace and blessings be upon him), the men entered a few at a time and prayed individually without an imam, until they had finished. Then the women entered and they too invoked blessings upon him (peace and blessings be upon him); then the children entered and invoked blessings; then the slaves entered and they too invoked blessings; and no one led the funeral prayer of the Messenger of Allah (peace and blessings be upon him) as imam.
Imam al-Shafi'i (may Allah have mercy on him) said: This was because of the greatness of his (peace and blessings be upon him) standing, may my father and mother be ransomed for him (peace and blessings be upon him), and so that people would not vie over one particular person leading the funeral prayer; rather, blessings were invoked upon him (peace and blessings be upon him) time after time.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الجنائز / 6907