You think worldly success is the problem?
How does that track? I'm trying to understand...
There must be, in the words of Roger Williams, a separation between Church and State, but "success" in the world for the Church has meant entanglement with government, and really pretty much all the modern ills suffered by the Church (when we understand from scripture that persecution
for the sake of the gospel is not an "ill suffered by the Church").
Roger Williams was a remarkable early American. He was on the second ship (after the Mayflower) bringing Puritans to America. He founded the first Baptist congregation in the Americas. He was also one of the first Abolitionists against slavery in America, just as slavery was getting started here. He was also a great friend to the Native Americans, evangelizing to them in their native languages while helping keep them from being exploited by other English settlers.
He founded the colony of Rhode Island explicitly as a state of complete religious freedom, including in his writings, "for the Musselman [Muslim] and the heathen [atheist]."
The reason he was so energetic about religious freedom was because he was a staunch Calvinist who believed in Election. For him, a person was either Elect or not Elect. If people were Elect they would respond willingly to the gospel. If they were non-Elect, they would never accept that gospel. So by his thinking, it was counter-productive to the government to entice or coerce people into becoming members...that would only pack the pews with people who didn't truly believe...and even put such people into leadership.
He therefore believed the Church should not have any sponsorship by the government. Further, as he looked at the history of government-supported religion in Europe, he counted nearly constant wars and atrocities, mostly Christian against Christian. Europe in his time had only recently emerged from the Thirty Years War and the English Civil War was fomenting. The English Civil War of state-religionists against Separatists (separation of Church and State) was soon to erupt.
Williams was one of those Separatists. He wrote the 1644 essay, "Bloudy Tenent of Persecution, for Cause of Conscience" outlining the evils perpetrated by the involvement of the Church in the business of government and vice versa. In fact, when Thomas Jefferson wrote about a "wall of separation between Church and State," Jefferson actually cribbed the line from Williams' work.
Williams made the point that Jesus always characterized the Church as being in tension with the world, not meaning the mountains, rivers, and forests, but man's kingdoms of the world.
Satan had offered Jesus control of the kingdoms of the world, but Jesus had resisted that temptation. Unfortunately, church leaders a few hundred years later fell into Satan's trap.
You adulterous people, don’t you know that friendship with the world means enmity against God? Therefore, anyone who chooses to be a friend of the world becomes an enemy of God. --- James 4
Williams' legacy extended into the writing of the Constitution. His state, Rhode Island, continued his ideology by refusing to ratify the Constitution until the First Amendment provision for the separation of Church and State had first been written and ratified.