People are concerned about a possible split in the Anglican Communion, all the Episcopal type churches that look to the Archbishop of Canterbury as leader. They make is sound like a complete disaster, but if it did come to that, it might not be altogether a bad thing.
Look at it this way. When Christianity first appeared, emerging among the Jews of ancient Palestine, the worshippers met in small house churches. They were usually outside the temple, and the synagogue. Jesus used a borrowed room for the Last Supper. The Christian Church as it then was, the body of believers, did not have a large formal infrastructure. There were no great processions of dignitaries, or massive majestic buildings. Jesus Himself said that the believers themselves are His house, the house of God, not some building.
I'm not suggesting that all Christian cathedrals, churches and minsters should be torn down. No way. They were built out of devotion to the Christian faith and to the glory of God. What I am suggesting is that there can be problems when the organized church becomes too centralized, and too structured under a hierarchy of human leaders. Human beings are only human, after all. No one of us should imagine that we can take the role of God in teaching or instructing others. Those called to teach need to teach purely from the Bible, not their own authority. Doing that can lead to the disaster seen in Jim Jones some years ago - and others besides.
If a large church split, and in its place there were small locally based house churches, then they might not have the influence that a large organization can have. But things would be more like they were in the days of the apostles, when post-Crucifiction Christianity was first coming into being.
One advantage of a large structured church is that it can share its resources, and do more with them (if the members are so inclined). It's easier to set up and run hospitals, schools, shelters for the homeless and welfare agencies like St Vincent de Paul, or the St John's Ambulance Brigade, with a large group of people who have money, labour and other things to contribute.
A disadvantage of a large church is, that bad ideas can be imposed on a large number of people. In the Middle Ages there was really only one Christian church, that which was centred on Rome. In those days the church taught that the world was flat and the Earth was the centre of the Solar System, with the Sun revolving round it. The Bible does NOT say those things. They come from the Ptolemaic science and cosmology of the ancient world, specifically Egypt. The scholars and thinkers of the time made the honest mistake of working those things out because that's how it seemed unless you had the advantage of modern equipment like a telescope and background knowledge which had not been learnt then. But the mistake the Medieval church made was to add those things to its body of Holy Writ - the things that the church taught as the Word Of God. In other words, they added things that are not in Bible to what they called the Word of God as revealed to humanity. They disobeyed the command the Bible makes not to add to what it says. They compromised the teaching that the Bible alone is God's Word. Thus a wrong, mistaken idea was imposed on the entire Christian world of the time.
The large churches of the world, such as the Anglican and Roman Catholic, have done some marvellous works. Try working out how many children have been educated, sick people cared for, homeless fed and sheltered and unsaved people evangelized by the societies they have set up and run. A small local congregation might not be able to do the same. So there is a good side to huge global churches. And there are some good things which could be shared when Christians communicate widely.
The argument is also used that small groups of Christians, isolated from others, can lapse into error without guidance. It's an overused thing in movies that a group of hillbillies out of touch with the world get carried away by mad satanic ideas. Things like "Children Of The Corn" use that in their plots. In might happen less in reality than it does in stories made up by people who want to discredit Christianity. And it can only occur if the people involved let it happen because they become proud or stubborn. A single Christian living alone can be kept from error if they read the Word of God honestly, and pray for the Holy Spirit to guide them. The do not need an archbishop or other dignitary to tell them what the Word says if God reveals it to them. Having said that, I know that Christians are encouraged to worship together and keep company to help care for and guide each other. But what is called 'strong' leadership, or authoritarian leadership, can have the effect of imposing bad teaching on huge numbers. As Jesus said, the leaven of the Pharisees can ruin a whole loaf.
It is in God's hands whether a large, influential church divides into smaller ones. I can't claim to know what's best. I can claim to know that it is NOT good to have unity by compromising the truth. If a church allows some of its members to carry on with practices that are not Christian, just to include them, then it is losing its integrity. If some Episcopal Church in the U.S. are disobeying the Bible by ordaining clergy who practice homosexual relationships, then it is futile to try and keep the Church together by allowing error or disobedience to God's Word.
The world is so huge that we can't have personal acquaintance with all the rest of its people. It's good for a Church in Alaska to have some fellowship with one in Scotland, or Australian Christians to have contact with African ones or anything you like. But Christianity existed before the whole world was known to the people of any one part of it. Some evidence exists that there was a Christian community in India since long before European missionaries went there. The Indian Christians received the Word without needing the big churches in Europe to get involved. Contact is good, but it is not essential. Human leadership has it's place but only under God. The Holy Spirit's guidance is the critical thing for believers.