One thing worth consideration is the very nature of the title Caliph. In practical terms, throughout history many have claimed the title, but few were widely believed to be a rightful Caliph.
This is not at all dissimilar to the Western Schism, when in the late 1300s there were three Catholic Popes. This has happened within Sunni Islam too. In the early 900s the remnants of the Ummayad dynasty seated in Cordobora; then Muslim Spain, claimed to be Caliph - at the same time as the Abassid dynasty was claiming the title given their control of the Levant.
So firstly, we have to realise that Caliph was never a concrete thing, it was fluid and could be interpreted as ecumenical or political.
Secondly, even the most obvious Caliphs; the Ottomans, claimed the title for centuries but never actually got around to putting this in writing until it became politically useful. In the 1700s territorial disputes with Russia allowed them to claim they were, as Caliph, the rightful protector of Muslims living in Russian lands.
It should be no surprise then that the Ottomans only became widely regarded as rightful Caliphs after they had became the Middle East and Muslim world's undisputed superpower. By this time other claimants had either died (in Spain) or been consumed (in the Levant) into the Ottoman empire.
Fast forward to the cold war and the character of the Middle East had changed. There was neither a Muslim superpower, nor the conditions for a theocratic system to emerge. The new zeitgeist was influenced by progressive and secular ideologies: American liberalism, Soviet socialism, Turkish Kemalism. Furthermore attempts to unify the Arab world failed.
You mention 1926. This was only a few years after the Ottoman empire fell, and Kemalism replaced Ottoman tradition. Widespread feeling was that the Ottomans had failed to adapt to the rapid technological and social changes in Europe, and had become the "Sick man of Europe". Alternatively the issue was that their failures were because of theological shortcomings. Either way, the old ways were no longer relevant and change was essential.
Egypt and Syria formed a United Arab Republic between 1958-71. In response Iraq and Jordan joined together and created the Arab Federation, as they were both Hashemite Kingdoms. But this lasted a mere six months. Libya's Ghadafi managed to create the Federation of Arab Republics, lasting 1972-7 between Libya, Egypt, Syria. And there have been many more unsuccessful initiatives during this era to unite Arab countries.
But this situation wouldn't last. The Middle East's Republics and Kingdoms became increasing corrupt and ineffective, and this provoked reactionary ideas. Islamist ideas, like those of Sayyid Qutb, started to take root after his execution in 1966. The Iranian revolution in 1979 would solidify the importance of religious politics in the Middle East. Since then the region has become more and more theocratic.
However, the region has also become more divided as nations attempt to prove themselves dominant, and sectarianism is out of control. Now there are many major powers, each having little hope of uniting the others; Egypt, Turkey, Saudi, Iran. Even minor powers behave with fierce independence, like Qatar.
Politically and religiously the Middle East has drifted apart. The bottom line is this: a Caliph would be agreed upon after political consensus; and nobody has been able to unite the Middle East politically since the Ottomans. Even with a Middle East more theocratic now than it has been for decades, without someone able to enforce unity no claimant Caliph will be taken seriously.