The reason that there has been so much corruption over the years in the Catholic church is theocracy.
It became a state bureaucracy that outlived the state that made it the dispenser of the state's charities and social services. when it became wealthy by the 12th Century it became a target for the 2nd sons of the nobility as a benefice seller, and its wealth became a target for bankers and monarchs.
When you mix the sinful activities of men when it comes to politics and power and then say God is at the helm, trouble starts. Constantine adopted the fledgling Christian religion as his own as a political ploy. He saw the new religion was spreading despite the persecution, so he figured it would be a good religion to adopt to use to obtain power. However, Constantine was not even a Christian. He continued to worship the same pagan gods he had always worshiped, although it is rumored that he converted on his death bed.
Actually he adopted it as an arm of the state because he admired their commitment to their faith and their successful social services programs. He was superstitious, and saw their resistance to the heavy persecutions under the previous Emperor and the other leaders of the tetrarchy as impressive and noble, while the pagans were obnoxious and dishonest. One of the other tetrarchs tried to get his pagan temple priest to copy the Christians' social services, Lucinius iirc, but they failed miserably, too corrupt an venal to pull it off. Being the more stable, he issued edicts preventing their persecution, at least in the territories he controlled. the other one continued to persecute Christians in his territories, until his eventual defeat.
He didn't 'rewrite' anything, he was too superstitious to do any such thing; the orthodox version that existed from the beginning was too well known for anybody to get away with such a thing for one, and for two after hundreds of years of being slaughtered by everyone around them, and with the very worst just occurring in recent memory and still going on, only idiots think they would have stood for any such thing, either; they were afraid of no one, and everybody knew it. It's complete rubbish that he demanded they change their bibles to reflect his wishes or anybody else's and they suddenly did so; only idiots will try and sell that stupidity as fact, as they were afraid of no one, especially Roman Emperors. It's a ludicrous claim, made by weirdos who want to rewrite the books themselves and make up rubbish they want to peddle, since they don't like the original theology they dream up lies they think will give credibility to their own rewrites.
Darrell Bock has an excellent little book for lay people on this issue re the orthodox versus the Gnostics and other fraudsters and the alleged '4th century Rewrites' fallacy. There were far too many copies around by the 4th Century for that idiotic claim to fly.
The Founding Fathers also saw this problem as they made sure no state church was created in America. They were tired of the state controlling people from the pulpit as they did in England.
Well, some felt that way, others didn't; the Baptists invented the concept originally, but some states did have a state religion they favored with privileges; the Constitution only limited the Federal govt. from interfering with the states' rights to do so. Massachusetts was the last to do away with their state sectarianism, in 1836 or so. This was due largely to demographic changes over the years in the states themselves, not Federal law.
And yes, given its history and origins as a government institution, the Catholic Church's bureaucrats do indeed favor it being a state religion again. They didn't really have much of a shot at that total control in the Middle Ages, though, despite all the noise claiming they did, since the individual feudal lords mostly appointed most of the Church officials in their own lands, and the Vatican had to pretty much go along with that practice, with only minor and temporary deviations over the centuries. Most of the peasantry and local nobility kept their local pagan pre-Christian superstitions and traditions, despite the lip service to the political realities. Even the monks noted this about the peasants on their lands; Europe was never all that 'Catholic' in real life.
The Salem witch trials come to mind in terms of the state and church getting together.
Politics and the struggle for power and money ruins everything.
Luckily, Christendom seems to have learned this lesson as where Islam has not. In fact, it is impossible to separate Islam from the state due to the need for Sharia law. They demand the witch hunts to continue.
A tiny event, noteworthy for its rarity in American colonial history, and the judge was sent from England; even Cotton Mather didn't like the outcome or believed in witches. It was just another case of peasants adhering to their pre-Christian traditions than informed Christians doing any persecutions; even the 12th century educated Catholics laughed at claims of ' magic' and 'witchcraft' as being peasant rubbish and superstition, and didn't exist in real life.
Christiandom learned this from its very beginning.