The Arafat day.

Assalamu alaikum.


On the 9th of Dhul Hajj, the holy Prophet (in person) stood up on the mount of Arafat and also delivered the sermon and lead on that Friday the Zuhr and Asr prayers. He also lead the Magrib and Isha prayers in Mudhtalifa. Was he standing for that Ibadat (Sunna) in the place of an Imam Kubra i.e, leader of the Muslim Empire/State and therefore a Political leader (in the example of the Children of Israel Yasusuhum anbiya'ahum) or in the place of Imam Sugra an ordinary Imam and not a political leader or head of state?
What positions did Abubakar, Umar, Uthman (I do not think Ali ever performed the Pilgrimage during the termoil) occupied on the day of Arafat?.
I mean did they stand as ordinary Imam (Imam Sugra) or Imam Kubra? Is it a sign of weakness, ignorance, arrogance or indifference to the Sunna for an Imam Sugra to lead the Arafat prayers?
Friendship.

Friendship wrote: ..........Was he standing for that Ibadat (Sunna).........

Those four prayers were Fardh.