Uthman b. 'Affan
Uthman ibn Affan (Arabic: عثمان بن عفان, romanized: ʿUthmān ibn ʿAffān), also known in English by the Turkish and Persian rendering Osman (579/583 – 17 June 656), was a companion of the Prophet Muhammad and the third person to occupy the seat of caliphate after the Prophet.
Simple search in Sunni books of Hadeeth leads to the fact that all the three whom you named ran away from the Jihad.
1. Abu Bakr:
Al-Haakim Al-Nisaboori who is one of the well known Sunni scholars narrated in his famous book Al-Mustadrak Alal Saheehayn, Volume 3, Page 37 that Abu Bakr ran away.
In Saheeh Bukhari and Dalaa'l Al-Sidq , V. 1, P.362 and Noor Al-Absaar by Shiblanji, P. 87, you find that Umar ran away.
Ibn Katheer (student of Ibn Yatmiyyah) mentioned in his books Al-Bidayah Wal Nihayah V.4, P. 28 that Uthman ran away.
Many other Muslims have also run away from the battles due to weakness in the faith. Only the firm and strong in faith stood fast and never ran away.
Exposing the hypocrites was declared in Quran by their deeds but not by their names. Same was done by the Prophet (SAWA) who did not expose their names.
The Prophet (SAWA) has clearly stated that many of his companions will change and turn back from right path after him then will be sent to hellfire. (Saheeh Bukhari, Hadeeth number 4259
and Saheeh Bukhari, Hadeeth number 6098,
and Saheeh Bukhari , Hadeeth number 6099,
and Saheeh Bukhari, Hadeeth number 6026,
and Saheeh Bukhari, Hadeeth number 6528.
A good book to read on this is The Succession to Muhammad [s] by Wilferd Madelung, who explains very clearly the subtleties of the political situation of 'Uthman. 'Uthman had incited fury among Egyptians, Kufans and others because of his nepotism and awarding his family property that belonged to the umma. He had also cut 'Aisha's stipend, angering her. The Egyptians came as a delegation to 'Uthman with their grievances, but he refused to listen to them. Instead, he appealed to Imam Ali (as) to tell them to go away. Imam 'Ali (as) warned 'Uthman more than once that in order to calm the situation, he must listen to their grievances and correct his actions. 'Uthman refused to listen, and so Imam 'Ali (as) distanced himself. 'A'isha sent out letters inciting those who were angry with 'Uthman to kill him. 'Uthman's palace was stormed. Interestingly, 'Uthman was abandoned by his cousin Marwan and his sons in his time of need. Imam 'Ali (as) sent just Imam Hasan (as) (not Imam Husayn) and some others to try to calm the crowds, but they went ahead and killed 'Uthman. Because Imam 'Ali (as) had not directly intervened, Aisha later took advantage of this and accused him of being responsible for 'Uthman's murder. She used this allegation to try to overthrow Imam Ali (as). Imam 'Ali (as) says in sermon 30 in Nahj al-Balagha that both parties were in the wrong: 'Uthman was wrong for misappropriating property and governing badly; and the Egyptians and others were wrong for murdering 'Uthman, basically meaning that the grievances should have been addressed through a legal process: "If I had ordered his assassination I would have been his killer, but if I had prevented others from killing him I would have been his helper... I am putting before you his case. He appropriated wealth and did it badly. You protested against it and committed excesses therein. With Allah lies the real verdict between the appropriator and the protestor.' Thus, in sending Imam Hasan (as) to try to calm the crowds, Imam 'Ali (as) was not actually siding with 'Uthman, nor supporting him, but was rather trying to prevent excessive and unlawful behaviour on behalf of the aggrieved parties.