Why did the Caliphate system fail. Why did it not continue until today. Don't you think we need one "just" leader for the whole ummah (World Muslim Community) ?

Whilst individual caliphates had their shortcomings, after all we are all human, as a ruling system it did not fail but was brought down when the Young Turk movement was helped by outside powers to conspire for its abolition. For more detail see the article: 

• From toppled caliphate to carved Turkey -  Common Sense issue 19.

Leadership is an essential requirement for any political order, and whilst Islam is open to various models of governance, with differing options for the authority, entitlements and obligations of the leader, the checks on his power, the involvement of subordinates in various decisions etc., there has to be an unambiguous command structure for such an order to be effective, and at the present time, with the Muslim entity divided into individual nation states, that is not the case. Leadership, however, cannot be imposed, a leader must emerge from his people by agreement.