When Ali (as) became the caliph...
When Ali (as) became the caliph, he did not see any benefit in getting it back himself, and did not want to be accused of using the (power of) caliphate for personal interests.
Also, perhaps he found that getting it back would have created problems from those who cried out 'O the sunnah of 'Umar' when Ali (as) changed some of the things which 'Umar introduced in the prayer of Taraweeh .[^2] Q7 - Fadak again: it is well known that Ahlul Bayt (as) did not care about worldly things, so why did Lady Fatimah (as) demand that the first caliph hand Fadak back to her? A - Fadak was a right for Fatimah (as), a gift from the Messenger of Allah or an inheritance from him.
It is natural for her to demand this right, without indicating a concern in money and worldly things. Demanding one's right, through natural needs and familial responsibilities, is a legitimate pursuit which is commended by Allah. That is the point. Secondly, demanding Fadak was a bridge to the caliphate, a legitimate right of which Fadak was one of its indications.
It was told that one 'Abbasid caliph said to Imam al-Kadhim (as): 'I am ready to return Fadak back to you, so set its boundaries', thinking that it was a mere area in al-Hijaz. However, the Imam said: 'If I set Fadak's boundaries you shall never give it to me.' The caliph asked: 'What are its boundaries?' He replied to him that the boundaries of Fadak were the boundaries of all the Islamic countries! Hence, Fadak was the starting point and not the goal.
Ibn Abi al-Hadeed - as quoted in his commentary on Nahj al-Balaghah - asked his teacher: 'Why didn't Abu Bakr give Fadak to Fatimah (as); if it was for the Muslims, wouldn't they have given it to Fatimah?' His teacher replied: 'If she was given Fadak, she would have demanded the caliphate for Ali, and therefore he decided to stop the matter at the start lest her demand would stretch to more than that.' Q8 - How can we reconcile the stances of Fatimah (as), when she died quite upset and angry with Abu Bakr and 'Umar, and that of Ali (as) who gave them bay'ah (oath of acceptance of rule)?
There are some people who are confused by this and would say that Fatimah (as) had been driven by emotions and that she got angry out of self-interest, while the stance of Ali (as) was rational? A - The stance of Fatimah (as) was the stance of Ali (as)! Ali's stance was negative and rejecting, just as Fatimah's was. Also, who said that Fatimah's stance was driven by emotion?