Yes, and I think it's almost more a matter of discipline. The reason I don't think the branch theory makes sense is because there is no inter-disciplinary understanding between the different groups. Thus even at a very practical level, your idea that branches should not develop contrary to one another is unenforceable. Such is much like an appeal to "international law." Dogma and doctrine likewise have no meaning or force apart from discipline. Of course current-day Protestantism has largely given up on discipline, and therefore tries to shape ecclesiological consciousness via "moral" persuasion. One could of course try to extend this to the branch theory, but I would say that the abandonment of discipline and the underlying structures and histories that guarantee that abandonment are the deeper problem.
I would say that someone like Martin Luther had no authority to set up a new church, and that set a foundational precedent where authority is unnecessary and discipline is impossible. Now compare this with Jesus the messiah and the questions and assertions of authority that constantly swirled around his ministry. The two cases, Luther and Jesus, contrast as significantly different bases for a religious movement.
Discipline and authority can be really tough nuts to crack. Without a willing social group, they become meaningless, whether in religion or in other areas of human life. Witness the various political revolutions that have occurred over time. Tyrants can only maintain their power and authority using brute force, which ultimately results in enormous fear and resentment among the populace which generally results in a regime change which, sadly, often creates a worse situation than the original one (e.g. various nations in South America).
Feudalism, as an example, was made to work by establishing strict class structures with the peasantry kept illiterate and dependent on their lords. With the development of a mercantile economy coupled with specific trades and skills among the peasantry there was more fluidity in the social structure which, inevitably, led to the Renaissance. As they say, the rest is history.
Another major factor is the concept of taxation. Without a monetary economy there is no thing such as taxation as in strict Marxism and peasants cannot earn wages, but depend on their masters for the basic necessities. When a monetary economy develops then the ruling class requires money to pay for a variety of things that government is believed to need, such as a standing army. When taxation reached a point of excess then the populace becomes quite restive. Both the American Revolution and its Civil War had made economic motives.
With religion one can see similar trends. Hinduism, with its strict caste system, continues to thrive, primarily because it is not structured to extort money from its adherents nor does it have any central authority to determine its beliefs and traditions. Spinoffs of Hinduism such as Buddhism, Jainism, or even Sikhism are generally viewed with passive indifference by Hindus. In the entire scheme of this system tradition, which is, on one hand, quite inflexible and unchanging, has no restraints imposed on it to prevent developments and alterations. If, for example, some Hindus decide to follow Vishnu, the followers of Shiva don't go to the trouble of bothering them, but allow them to erect their temple, according to their ability to raise funds from the upper castes. The trouble comes when foreign religions such as Islam and Christianity attempt to upset the social order and insist that, at the command of their God, Hindus must abandon their faith and traditions and serve one God exclusively or face severe consequences.
Returning to Christianity, although one can make an argument that there must be a sole center of authority and discipline in order for the system to survive and, possibly, thrive, history has shown otherwise. The Eastern Orthodox Churches, despite lacking any form of a centralized authority, have survived despite intense persecution both from Islam and from the Roman Church. Tradition has been a huge factor in its survival. It does not have the luxury of molding its tradition to suit prevailing trends both within and outside of it churches.
Part of that might be things like "the new perspective on Paul," where the Jewish and liturgical roots of Christianity are becoming more widely recognized among Protestants. Also, the idea of "tradition" is becoming a lightning rod for a culture which moves and changes ever more quickly. Different forms of societal instability will drive people of all kinds to seek out anchors of tradition where they can weather the storms.
It seems to me that there is a deeply rooted psychological need for stability, which includes routines, both in life and in religion. This has various manifestations, as in the seven-day week with one day set aside for rest. Ritualism also plays into this need. In the past, the need for religious ritualism within Protestantism was not adequately met by its relatively cerebral services. One of the results was the development of Freemasonry which was initially quite popular across the religious spectrum, but was condemned both by Catholics and Lutherans who seemed threatened both by its religious content and its elaborate ritual. Now that Freemasonry is in a death spiral, other forms of ritualism are being tapped.