doubt we will ever really get to the bottom of this but I saw the Church being as down on the Gods and Goddesses of Greece and Rome where as yes, in England the kings were vying for the position of power.
As to the Church that is an interesting story that because they became so powerful the story is told to fit the narrative - having spent years looking into early church history that at the same time I happened to be reading the history of those tribes that were later to make up German, Netherlands, Belgium and France - actually I was trying to find when all this Jewish hatred started and I think I found it - anyhow in the process in the Cambridge Illustrated History of Germany there is an easier to read account (elsewhere as well but so much thrown in its difficult to sort out)
Seems from 479 to 485 the Visigoths were the most powerful in Europe as was their King - The Visigoth king codified law that included kings should die a natural death. Euric's was not willing to wait and hooks up with the Frankish King Clovis whose wife was a Christian and converted Clovis - Christianity had not stopped Clovis from all the slaughter typical of the times however, during his reign many a monistary was built in what is now Germany - After the death of Clovis his sons inherited his 'kingly grace' which the belief was special ancient blood flowed in their veins that made them magical and if they walked for instance on a field they could make crops grow.
However, they were lazy and when the Franks came along and it was a battle over both the hero worship of Saint Martin of Tours, an ordinary soldier who became a monk and later a Bishop was supposed to have met Jesus who disguised himself as a beggar and Martin shared his cloak that was revered as the Merovingian King's most powerful relic versus the Franks knowledge of how to bake bread, lay bricks, blow glass, make iron farm tools - this back and forth continues on into the time of the Carolingians when Charles Martel's basterd son Pepin III is made king - although Martel conquered most of the tribes in Europe the magic and St. Martin of Tour's cape gave the Merovingian kings more power and so Pepin gets the bright idea to be crowned by the Church whose grace and power come directly from God. Tra la Through this act the Church was given more power as being equal in overseeing and governing most of Europe.
Now inside Rome the Church again came to the rescue - as Rome was falling apart the everyday city services were no longer available, like garbage collection - but more important there was no codified law - the Roman kings and emperors were the law and administered what law was traditional. There were lots of land disputes and paternity disputes that gradually the people could go the the Church courts and have a judgement and so little by little as Rome fell the Church filled the breach without really a plan - (looks like where ever there is law that gives you the upper hand) the huge change in power came about with Constantine.
Lots of early alliances, battles, joining his father in France to cross and take on, winning a battle in what is now York followed by more good moves towards cementing power there is this..."After his victory over Licinius in 324, Constantine wrote that he had come from the farthest shores of Britain as God’s chosen instrument for the suppression of impiety, and in a letter to the Persian king Shāpūr II he proclaimed that, aided by the divine power of God, he had come to bring peace and prosperity to all lands." He is instrumental in getting the church to declare the Council of Nicaea which formed the basis for what we know today as the Roman Catholic religion and laid the ground work for the Church, when adding the power it assumed by crowning Pepin III, to be the Holy Roman Empire.
The Council is when the final nail is in the coffin of followers being officially called Christians, where as, they had been known as followers of Jesus and were basically Jews. Although the word Christian had been bandied about since just before the year 200. Constantine came to power in the very early 300s, the First Council of Nicaea, 325 where the 'Roman' Catholic Church became official as it officially separated from Constantinople and the Eastern Orthodox Church.
The first universities were built in the 11th century (Bologna 1088, Oxford 1096, Cambridge 1209) and so if you wanted an education you had to become a Catholic Priest - that did not mean you practiced your priesthood - many like Petrarch, poet (born 1304) and his brother did not. However, education was only available and later predominately in the monasteries. This carried on into the new World - e.g. Fordham Prep (High School for boys) and Fordham Univeristy in NY, a Jesuit monastery.
Back to Constantine - his earliest moves was to donate land and buildings to the Bishop of Rome - and that is another story how all churches at first had to have a bishop anointed and assigned by the Pope and a relic (body part) from the earliest sainted followers of Christ and of course having a piece of the cross was tops. In and around Rome there were something like 140 churches and these Bishops eventually became the first Cardinals.
After all that I am seeing your thought that education controlled by the church would have an influence however, why the emphasis on learning Greek and Latin - even when I went to school most Catholic high schools required you take 4 years of one or the other and sometimes both - which meant translating all those ancient stories - was that it - the middle age stories about knights and their code was written in a colloquial language (English, Welsh, French) as compared to what had been established for several hundred years as classical language?
