In the East, there was much less centralization. As Rome became the enter of the ecclesiastical world in the West, Jerusalem, Antioch, Alexandria, and Constantinople remained autocephalous in the East. Independent churches then emanated from Constantinople, but they quickly broke off. The Patriarchate of Bulgaria became independent as early as 927 with others following suit. Thus, national churches were an inherent part of the East which did not have the autonomy of Rome and was much more organic in development.
As papal power grew in the West with the increase of ultramontanism, there were notable holdouts. The Church of Utrecht, for example, resisted the papal imposition of a bishop in favor of their charter which required an election by canons. Ultimately, the Church of Utrecht was joined by the Old Catholics in 1870 who implemented national Catholic Churches in what became Austria, Germany, Switzerland, the Czech Republic, etc. Yet the spirit of the Low Countries permeates these churches as the motherland of the Old (Roman) Catholic tradition.
In 1945, the Old Catholic Churches were joined by the Brazilian Catholic Apostolic Church and Dom Carlos Duarte Costa. Duarte Costa was in favor of the national model, with the goal of creating a church for Brazilians that was imbued with specifically Brazilian features such as Portuguese in the liturgy, etc. Yet, as early as 1948 Duarte Costa consecrated Castillo Mendez for the work of the church in Venezuela. He saw the benefit of the national church model and promoted its spread throughout South America.
In addition to the (former) Roman Catholic and Orthodox national churches, there remained the Anglican churches which were built on a national church model (with deference to Canterbury). As with Rome, independence was first rebuffed. But, the rebellious colonists sought out the help of Bishop Samuel Seabury who helped them establish the first church independent of the Church of England outside of the British Isles (with the assistance of the Scottish Episcopal Church).
There are many challenges with national churches. First, national churches can promote nationalism as we have seen in some of the Orthodox countries. The state church can become enmeshed with the government in ways that make them indistinguishable and ultimately harm the credibility of both. Second, national churches can take on the causes of the nation. Thus, the loss of ecclesiastical territory becomes a matter of national pride. The unfortunate situation then occurs where there are multiple churches of one tradition competing on the same soil, all while anathematizing the others. National churches can be difficult to hold together in a meaningful form of worldwide communion. The Anglican Churches are evidence of this, as the ordination of women and LGBT people becomes more problematic for sister churches. The same occurred in the Union of Utrecht, when the Polish National Catholic Church pulled out over the ordination of women. In short, egos, territory, definitions of heterodoxy, and other issues stymie national churches in ways that do not affect Rome.
However, there are not only negatives. National churches do join the social fabric of the nation. They knit together people so that they have a common destiny and have their own self-governed church. This church looks like them, speaks their language, and has their interests at heart. There are ways to mitigate heterodox beliefs by ensuring that there is some sort of common communion, as with the Eastern Orthodox Churches. They don't always like each other (they frequently dislike each other), but there have been ways in which they have worked together in the past (notably when America was establishing its Orthodox presence). Like everything, national churches have to act intentionally and not independently. But, some would argue that this hinders prophetic calling and witness when one group is moved to act in one way but the other churches disagree.
It will be interesting to watch how Rome handles recent developments with local independence. As Pope Francis is committed to the synodal path and promotes national episcopal conferences, there are rumors of fractures already forming. The German Church, for instance, seeks to bless same-sex unions. Rome has said it is verboten, but what will be the outcome if there is a walkout? Will national churches become more favored as Roman Catholic dioceses become increasingly independent in charism? The Orthodox have managed to keep themselves together, more or less, but it has been with common agreement and with an Orthodox phronema that you don't have to define everything. Rome has boxed itself into a corner by defining every article of belief, such that deviation is not permitted. How will Autocephalous Catholics be affected by Roman changes and how can we avoid the pitfalls while promoting the good?
Ultimately, as Autocephalous Catholics, I believe that national churches are a common form of structure of all of us. ICAB, Old Catholics, Continuing Anglicans, etc. all hold the concept of national churches even if they differ in liturgy and understanding of doctrine. I do not think that the concept should be abandoned, because I believe it is a good one and one to which I am committed. And, I believe that we have to work together as national churches. There are too many similarities between us. The structure of the Church should be accessible to the people and local enough that they have participation in its outcome. But, ideally this should be done in the spirit of "in necessary things unity; in uncertain things liberty; in all things charity."
"In the first century the Christianity, the national Churches lived and developed in complete autonomy, without being vassals to the Bishop of Rome. I call to your attention to the testimony of Tertullian who said: "Our many churches considered themselves as all belonging to one church, the first of all founded by the Apostles and mother of the rest. They are all holy and apostolic and, together, cannot be looked upon as anything by a singe entity, whose message of Peace, whose mutual brotherhood, whose bonds of charity unite all the faithful." - Manifesto of Bishop Carlos Duarte Costa