It is not the case by a long shot. In Anglicanism there is no agreement on the sources of authority. Some say the Bible. Some say the Bible and tradition. Some say the Bible, tradition and reason. There is no agreement on the sacrament. Some believe it is a symbol. Some believe it is a metaphor. Some believe it is the body and blood of Christ. There is no agreement on ordination or the ministry. Some think a priest is a preacher. Some think a priest is a social worker. Some think a priest is a Protestant minister. Some think the priest is a sacrificing successor of the apostles. Take it from me. In one Anglican parish on Sunday the priest consecrates the host and reserves the remainder for veneration in the tabernacle while the priest in the next door parish says the same words, but then sweeps out the crumbs afterwards for the birds. You say there is the same division in the Catholic Church as in the Anglican Church, but with respect Father, it is simply not true.”
There are differences of opinion in the Catholic Church, but there is an organic unity of belief and doctrine that transcends these differences of opinion, and this underlying unity is upheld and maintained by the ministry of Peter.
To put it simply, “Rome has spoken. That settles it.”
This universal apostolic authority provides the foundation, the rock on which we build. It provides the basic ground of agreement on the basics even though we disagree on the details.
For a church to be universal and contemporary in application it must have in infallible authority.
In other words, to be able to adapt and change where she must and resist change where she must, the church must have a final arbiter.
Otherwise it is up to every man with his Bible…and that is what we call Protestantism.