Why did no one lead the people in prayer as an Imam over the Prophet (peace be upon him) in the funeral prayer?

The Companions prayed over the Prophet, peace be upon him, individually, not in congregation, for several reasons mentioned by scholars, including:

1. The Prophet, peace be upon him, commanded it, though this has not been authentically narrated. 2. The Companions' eagerness to attain the virtue of praying over him, their concern for unity, and their reluctance for anyone to lead the prayer before the matter of the caliphate was settled. 3. The Companions' desire to obtain the blessing of praying over him individually and privately, without being subordinate to an imam. 4. Out of reverence and respect for him, and awe that anyone should step forward to lead the people in prayer over him.

It is permissible to perform the funeral prayer individually; congregational prayer for it is a sunnah, not a condition for its validity.