Please read this interesting narration in Sahih Muslim.
When Umar bin Khattab was in his last days of life. His son Abdullah bin Umar came to him and said:
"They presume that you are not going to nominate a successor. If a grazer of camels and sheep that you had appointed comes back to you leaving the cattle, you will (certainly) think that the cattle are lost. To look after the people is more serious and grave. (The dying Caliph) was moved at my words."
http://www.sunnah.com/muslim/33/14
Please read more details about this matter
If we say it was not needed, then why the companions of the prophet got together soon after the death of prophet to make someone as a caliph? They even left the dead body of the prophet unburied and finished the matter of Caliphate (Tabari and others).
Does this mean that the selection of the next leader was very important matter to the point that it became even more important for them than burying the dead body of the prophet?
If the answer is yes, it was an important matter: then why the Prophet (pbuh) did not address this matter? It brings an objection to Prophet Mohammad that he did not take care much about his nation?
While the real situation is very different! This is proven that Prophet Mohammad in his last days, he was very sick, (this narration is also in Bukhari) he appointed Osama bin Zaid as the commander of Islamic army. (Osama bin Zaid was a young man, Abu Bakar and Umar were also included in that army under his command) whenever the prophet used to get little bit better, he used to ask about that army if that army is gone already?
The companions of the prophet hesitated to join under the command of Osama; the prophet got angry and told his companions to join Osama's army and they must go. In the history books it says that the prophet cursed on those people who hesitate to join the army of Osama.
(Actually Prophet Mohammad (pbuh) wanted to send those people outside of Medina, those who wanted to form their Government after prophet's death).
Prophet Mohammad (pbuh) used to take care of his nation so much; we already gave an example. In that example we can also see that the prophet put Abu Bakar and Umar under the command of a young person named Osama bin Zaid, how come the Prophet would make Abu Bakar as the commander of all Muslims?
The whole life of Prophet Mohammad testifies that Prophet Mohammad used to appoint the head of tribes, head of groups, even whenever he used to send few people; he used to make sure that there will be one person who will lead the group.
It was very important for Prophet Mohammad (pbuh) to appoint the head of his nation to save them from any kind of destruction and division.
By that time Islamic government was newly formed. There were lots of anti- Islamic forces who wanted to destroy Islam, for example there were lots of hypocrites, many verses in Quran tell us about them.
“Some of the desert dwelling Arabs around you are hypocrites as are some of the inhabitants of Medina. They are persisting in their hypocrisies. You do not know them but we know them well and will punish them twice over. Then they will be brought to the great torment (on the Day of Judgment)."
-Quran 9:101
There were Jews; there were Romans and Iranian empires wanted to destroy this newly formed Govt. in Arab region.
It will look as if Prophet Mohammad (pbuh) had no political vision (Astaghferullah) if we believe that he did not appoint anybody after him.
We know in the entire human history that all supreme leaders and head of nations appointed someone to be the leader after them. Even for example somebody who has goats and sheep, he makes some arrangement for goats and sheep before he leave.
If we believe that Prophet Mohammad did not appoint anybody after him. It means that Prophet Mohammad did not have vision like a common person (Astaghferullah).
The first prophet and first human being on earth, the father of humanity ADAM (as) appointed his son Sheeth after him. (History books Tabari, History of ibne Kathir etc).
Prophet Moses(pbuh) goes to Mount Sinai for forty nights. He appointed his brother Aaron, to be the leader of his nation. (Quran)
How come the Prophet who is going to leave his nation forever will not appoint anybody to be a leader after him? While Prophet Mohammad did not have an accidental death!
We know very well that The Holy Prophet (pbuh) who guided with revelation knew very well that what is going to happen after him. The Holy Prophet warn his companions that many afflictions will happen after him, Please check the chapter of Afflication in Sahih al-Bukhari. It means that the Prophet (pbuh) did not make any arrangement to save his nation?