Did Prophet(pbuh) chose someone as Caliph !

religion and politics are inseperable in islam, even if u are sunni u think abu bakr & umar were merely political leaders?.

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If we had a clean slate to start over, And Ali rah was the first Khalifah, who should have been the next Khalifah?
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thats a hard one, ....even Ali died in 40 AH his supporters unanimously elected Hasan, Ali did not appoint anyone
if ALi had been first caliph he was the youngest of the 4 ...so assuming he died early like 30 AH there are still many senior companions alive anyone of which cud be caliphs abubakr & umar though wud likely be dead by that time
secondly under Ali is unlikely that Quraish solely held the right to caliphate as ALi had appointed a lot of non-quraishi or ansars to high posts [including his successor at one time] ...so it very likely that a medina ansar might have been a second caliph