So this is an intriguing question insofar as the situation in 800 presents itself. Some background is needed to understand why Pope Leo III took the steps he did, and ultimately crowned Charlemagne as the Roman Emperor. It should be recognised that Charlemagne was crowned as Roman Emperor, the Holy coming along later to denote the circumstance in which the title was conveyed.

Prior to the 700s (and perhaps slightly into them), the Papacy was generally considered to be under the protection of the Eastern Roman Empire. However, general issues of increased Eastern Roman interference in Papal affairs, alongside a move towards Iconoclasm in the 720s led to a break in relations between the two entities. This issue of Iconoclasm caused significant tensions between the two entities to be more exact, and Emperor Leo III did attempt to send a force to pacify Pope Gregory III and bring the Papacy back under control. And depending on the source, by 730 Pope Gregory III had excommunicated Emperor Leo III (Theophanes establishes this, though there is seemingly no record of this in the Liber Pontificalis). These tensions meant that Gregory III's successor, Pope Zachary, did not seek the consent of the Eastern Roman Empire (specifically the Exarch in Ravenna) for his election, becoming the first to do so in the Papacy's history and setting a new precedent in Papal sovereignty. At the same time, it should be noted that the Eastern Roman Empire's physical influence over the Italian peninsula was waning. This impacted its ability to protect the Papacy from the Lombards, who were rapidly advancing into the peninsula. Pope Gregory III had actually attempted to push Charles Martel to intervene in the issue, a precursor of what was to come. These religious and military issues set the backdrop for what in and around 800.

Moving forward, these precedents and issues become more solidified. Pope Paul I had become the first Pope to announce their election to the Franks (specifically King Pepin, father of Charlemagne). And by Pope Adrian I in the late 700s, the Papacy was no longer dating its documents in the years of an Eastern Roman Emperor's reign, rather utilizing the standard 'under the rule of Our Lord God and Saviour Jesus Christ, God the Father Almighty, and the Holy Spirit throughout all ages'. This move towards independence was increasingly fueled by practical realities. The Lombards continued to be an issue for the Papacy, and this culminated in 772 when the Lombards under Desiderius invaded the Papacy. Unable to look towards the Eastern Roman Empire for protection, Adrian I sought aid from the Franks under Charlemagne, who destroyed the Lombards. The explicit protection that Charlemagne was able to provide the Papacy plays a significant role in why Pope Leo III chose the actions he did.

Now onto the meat of the question. The period surrounding 800 differed in context to earlier periods. The Eastern Roman Emperor was Irene of Athens, who had become sole ruler after the ousting of her son Constantine VI in 792. Irene had worked to conspire against Constantine, having him ousted and eventually blinded with other co-conspirators. Her ascension to the throne presented a unique situation. The Roman Emperor was a woman, who in many people's eyes had usurped the throne and had played a part in her son's death. For Pope Leo III, the seat of the Roman Emperor was essentially vacant (both in part to the way in which Irene had come to power, but also due to her being a woman). This situation provided the Papacy and Leo with the ability to circumvent the power of the Roman Emperor, establishing Papal sovereignty while ensuring protection from external threats. As such, Leo III went forward to crown Charlemagne. While this conferred a significant air of legitimacy onto the Frankish king, it also was incredibly significant for the Pope. Through this action, the Pope had essentially broke against Roman precedent. In the Eastern Roman Empire, "the emperor’s coronation by the patriarch followed upon election by the army, senate, and the people". Pope Leo had instead bonded Charlemagne, and the title of Roman Emperor "to his own person, to the see of St Peter, and to the Holy Roman Republic". What should be noted as while there was little precedent for the Pope crowning a Frankish king Roman Emperor, it wasn't something which occurred spontaneously. As noted, it had stemmed from nearly a century of increasing disdain between the Eastern Roman Emperor and the Papacy as well as a need to establish Papal sovereignty while still retaining military protection. Irene's accession to the throne provided Pope Leo III the circumstances needed to move the crown, at least in his eyes and the eyes of the Franks, from the Eastern Roman Empire to the Frankish one.

In regards to the reactions to the coronation and the interpretations, there are a few relevant ones. Firstly, Pope Leo III's. It should be noted that Leo did not intend to "engineer a deliberate split in the Roman Empire, still less to bring about to rival empires where one had been" and rather was intending to establish the continuation of an empire which he believed was now vacant (though the consequences of his actions do deride his intentions). In the case of the Charlemagne, Notker the Stammerer states that the new Emperor felt that "the Greeks would be filled with even greater jealously than before, and that they would plan some disaster for the Frankish kingdom". Charlemagne seemed to feel as though the coronation would cause an irreversible conflict between his empire and that of the Eastern Romans. For the Eastern Roman Empire, the issue this caused is readily apparent. The Roman title has seemingly been usurped by the Franks, and it seemed to them that their continuation of the Roman Empire was being challenged. Einhard specifically notes that the Eastern Romans had a saying, that "if a Frank is your friend, than he clearly is not your neighbour". The interpretations are pretty clear-cut, at least for the major actors in regard to this event. Charlemagne and Pope Leo III were cautious of the issue this would cause with the Eastern Roman Empire, though were confident enough that their actions would stand to scrutiny, whereas the Eastern Roman Empire was infuriated by their actions.

Overall, what should be noted is that while Pope Leo III's actions do not necessarily have precedence (both in the case of the usual procedure for elevating a new Roman emperor, as well as the case of the Pope being the one to do so), they aren't actions which occurred without thought. The coronation of Charlemagne occurred due to a combination of long-term factors regarding the relationship between the Papacy and the Eastern Roman Empire, as well as the immediate context which had made itself apparent to the actors involved. The actions taken by Pope Leo III had the expected consequences in regard to all involved, and this would play a large influence in the Schism between Eastern Orthodoxy and Roman Catholisicm.

Sources Used:

- Einhard, “The life of Charlemagne.”, in Two Lives of Charlemagne, ed. Lewis ThorpeHarmondsworth: Penguin Books, 1969.

- Notker, “Charlemagne.” in Two Lives of Charlemagne, ed. Lewis Thorpe Harmondsworth: Penguin Books, 1969.

- "Liber Pontificalis”, in The Coronation of Charlemagne, ed. Robert Folz, London: Routledge & Keagan Paul, 1974.

- Noble, Thomas F. X.. The Republic of St. Peter: The Birth of the Papal State, 680-825. Philadelphia: University of Pennsylvania Press, 1986.

- Folz, Robert. The Coronation of Charlemagne, trans. J. E. Anderson. London: Routledge & Keagan Paul, 1974.

- Ullmann, Walter. “The Coronation and Papal Concepts of Emperorship.” In The Coronation of Charlemagne; What did it signify, ed. Richard E. Sullivan. Boston: D.C. Heath and Company, 1959, 70-79.

- Ohnsorge, Werner. “The Coronation and Byzantium.” In The Coronation of Charlemagne; What did it signify, ed. Richard E. Sullivan. Boston: D.C. Heath and Company, 1959. 80-91

- Norwich, John Julius. Absolute Monarchies. New York: Random House, 2011.