To make a very long story short, the Byzantines had more enemies in the 10th century than just the Abbasids. Around the period of Antioch's successful capture, the Fatimids had just completely conquered southern Italy and Sicily and Sviatoslav I of Kiev had just conquered Bulgaria and was now encroaching on Byzantine territory.

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So the initial Muslim conquests stripped the Eastern Roman empire of Syria, Palestine and Egypt in quick succession. ... Hadn't the Abbasid caliphate fractured by that point?

Yes, and the Rashidun and Umayyad Caliphates also captured much of the former Sassanian Empire. This was because the Byzantines and Sassanians had both exhausted their strength through near-endless warfare against each other. Do bear in mind: the last Byzantine-Sassanian war was from 602–628 while the Rashidun Caliphate began its conquests in 632. This is a very different situation from the gradual fracturing of the Abbasid Caliphate to the Fatimids, Buyids, Seljuks, and semi-independent emirates like the Hamdanid Emirate of Aleppo. The most obvious parallel to the declining of the Abbasids' power was the concurrent fracturing of the Carolingian Empire in Western Europe.

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What stopped the byzantines from capturing Jerusalem?

Iōánnēs I Tzimiskēs tried during a campaign through the Levant in 975. His forces had captured or raided (the sources are unclear) numerous cities in the Levant, but they failed to take Jerusalem. He died while returning from that campaign and his nephew and co-emperor Basil II, had a virtual civil war to deal with before he could think turn his attention back to the Levant. That period of civil war meant that most of what Iōánnēs had gained in the Levant was also quickly lost.

If you want to know why Iōánnēs waited so long, it's because after overthrowing Nikephoros II Phokas with the help of the conqueror of Antioch, Mikhael Bourtzes, Iōánnēs went on a campaign to stop Sviatoslav I of Kiev and didn't turn his attention to Abbasids until 972 when he led an invasion of Mesopotamia.

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or sacking Baghdad

Baghdad was conquered by the Persian Buyids in 945 and they were more than willing to defend the city against any other invaders, even though the Abbasid Caliphs at the time were basically figureheads.

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Since in the 900s three of the cities were then under Muslim rule (Alexandria, Antioch, Jerusalem), did restoring the pentarchy (politically) factor in Byzantine strategy at that time?

It wouldn't surprise me if it was still on some people's minds, even though I don't know if it ever was officially promoted as policy. You have to keep in mind that the unity of the Pentarchy had already been shattered on account of the 5th century Chalcedonian schism, due to a lot of Christians under the patriarchates of Alexandria and Antioch rejecting the Council of Chalcedon's favoring of Dyophysitism over Monophysitism or Miaphysitism. (These are theological concepts about the nature of Jesus Christ that are too long to get into here.)

As it was, by the 9th and 10th century, most Byzantine writers on the Pentarchy were taking the view that Constantinople was the highest of all the patriarchates regardless, rather than treating them as equals and the Roman popes were also claiming superiority, which was one of the causes of the Great Schism of 1054.

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Sources:

Bosworth, C. E. (1975). "Iran under the Buyids". In Frye, R. N. The Cambridge History of Iran, Volume 4: From the Arab Invasion to the Saljuqs. Cambridge: Cambridge University Press. pp. 250–305.

Kaegi, Walter Emil (2003), Heraclius: Emperor of Byzantium, Cambridge University Press.

Norwich, John J. (1991). Byzantium: The Apogee. Alfred A. Knopf, Inc.

Pourshariati, Parvaneh (2008). Decline and fall of the Sasanian empire: the Sasanian-Parthian confederacy and the Arab conquest of Iran. I.B. Tauris.

Walker, Paul E. (1977). "The "Crusade" of John Tzimisces in the light of new Arabic evidence". Byzantion. 47: 301–327.