I am, in fact, but by the Anarchy the principle of dynastic succession had been firmly entrenched by the Umayyads and Abbasids over more than two centuries, so it was very unlikely to be reversed at that point. Therefore the size of the Caliphate afterwards is irrelevant. What was important was the size of the Caliphate during the era of the Rightly Guided Caliphs, the Umayyad period, and the early Abbasid period. By expanding to conquer much of the Roman and Persian Empires, and stretching from the Indus to the Atlantic, it removed all of the conditions needed to sustain a republic during the pre-modern era, and substituted those favoring a monarchical principle. Even had the Umayyads not been, well, the Umayyads, it was going to be very difficult to maintain anything but the pretense of elections under those conditions.
The easiest way to have a republican Caliphate, as I said, would be to have Islam be far less successful against Mecca, just holding on but not able to overcome its opponent. If the Caliph only controls Medina, then, as I said, a republican constitution is far more likely than if he must contend with events across a third of Eurasia.
I definitely understand the point you are making. It is perhaps correct that the Khilafah if remaining small and contained within a small space, would be more conducive to some form of plutocratic reform. However, from my readings, it is more clear that the ideals of a more equal Khilafah and the notion that the Caliph abd his Ulema were infallible came from the conquest of Arabia and subsequent territories. No reform would be made as all within the Caliphate would be relatives of the Sahaba and Hijazi Arabs, ideas that came later that would lead to a true republic were elsewhere, had the Caliphate remained in the Hijaz, the power of the Ulema and the infallibility of the Amir al-Mu'minin would be firm, these two would be a check against each other, however this is not a republic in the same sense.
1. The ideals as espoused by the Khawarij, beginning with Bedouin inhabiting the Najd up to Iraq where the first to espouse a seemingly more egalitarian tone. By this I am speaking on how in Islam it is forbidden to rebel against the Khilafah and traditionally go against the the Ulema and further to commit Biddah of the Deen changing the law and decree of Allah. These factors limit the growth of a true Democracy as power is held completely by either the Caliph and or the Ulema, who have no intention of sharing that power of Hukm.
"Oh you who believe, obey Allah and obey the messenger and those in authority among you" (Quran 4:59)
"The best of your rulers are those whom you love and they love you. You pray over them and they pray over you. The worst rulers are those whom you hate and they hate you. You curse them and they curse you". They said, 'O messenger of Allah (SAW) shall we fight them and oppose them over that?' He replied, 'No, not as long as they establish the prayer among you. If someone is appointed over person and he sees some act of disobedience to Allah from him, he should dislike what he does of disobedience to Allah but he should not remove his hand from obedience.'" -narrated by Hazrat Auf bin Malik (RA)
Shaykh Ibn Taymiyyah says:
"This clarifies that the leaders, who are the rulers and those in charge of the affairs, are to be disliked and rebuked whenever they bring an act of disobedience to Allah. However, one does not remove his hand from obedience to them for the sake of Allah. It also shows that some of them are righteous and others evil."
Now, with this said, the above is the Aqeedah in relation to the rebellion of Ahl Sunnah wa l'Jama'ah, rebellion and the removal of a leader for anything but Kufr Akbar is clear cut not permissible. If the Khilafah remains in Madinah, then these rulings go most likely unquestioned and the authority of the Ulema supreme.
The Khawarij on the other hand, supported a system in which the Khilafah and the Ulema were equals to the slave, claiming an Ethiopian slave was equal to the Amir al-Mu'minin in piety (in the traditional Fiqh this is false) and the Ulema was not infallible in their rulings. Further, they did not just speak on this but they acted, as was seen in the Zanj rebellion. Creating a highly inclusive form of system made up of the minorities in the Caliphate who were left behind by the "noble" Mu'Tazila and the Ulema. The first sign of Khawarij and in reality a libertarian sense of rejection of authority and infallibility comes from the Qurra tribe in its response to Muawiyah (they had refused the Zakat):
"How much you go on about the authority of the Quryaish! The Arabs were eating from the hilt of their swords while the Quryaish were nothing but merchants!" He then said, "As for the shelter you mentioned, when the shelter is pierced, then come to us."
This ideology of resistance to the Khilafah and the will to create a system different than the traditional Khilafah would not have existed had the Caliphate not expanded outside the mind of the traditional Hijazi Arab.
2. Other than the Khawarij, the Murji'ah arose as well from the Fitnah as a group. They proclaimed that no person, even the Ulema or the prophet himself could make Takfir. This led to a deep questioning of authority and the same will (but in another direction) for a new and more egalitarian system. This mode of thought seen in the Murji'ah would not exist had the Hijazi Caliphate not expanded into the Najd, Iraq, Syria, Iran and Africa.