That's not how it works among Protestants, since there are as many interpretations as there ae members, and since there is no concensus that must be followed.
So, your comparison is invalid, imo.
As far as continuously being in a state of fragmentation - that is NOT a basic and elementary fact, though you would like it to be. Some denominations are quite stable
True, but the number of splinter groups is growing without any sign of slowing down. There are currently over 33,000 registered "denominations" outside of the Catholic, Orthodox, and mainstream Protestant Churches, and growing.
Yes, they have variety within; but the Baptists, Methodists, Episcopalians, Presbyterians, & Lutherans (and others), have existed since at least the 1700s, many quite earlier
Most of them were actually 19th century offshoots. The original ones are Lutheranism, Anglicanism and Calvinism. Anglican Church, which was founded by Henry VIII, was essentially Catholic (except for recognizing the Pope as the head of the Church) until Lutheranism, when it accepted certain Protestant beliefs.
Catholic and Orthodox teachings go back to the earliest days of Christianity and follow the same path for the first 1,000 years as an undivided Church. Orthodox Divine Liturgy is 1,600 years old. What's your point?
Baptists are traced at least back to the 1600s. Anabaptists lived during Luther's time though their theology varied. Mennonites have a strong kinship with Baptists as well. Methodism was an offshoot of anglicanism in the 1700s through the Wesleys. Likely a strong puritan kinship there as well. Beyond that, Protestant beliefs can be seen stretching throughout history. While Catholicism was by far the majority belief from the 300s forward, they weren't the only game in town. Unfortunately, they had a tendency to burn other people's writings so some of the beliefs of other groups such as the Petrobrussians, Waldensians, Lombards, etc., are lost. We may have some pronouncement against them by the Catholic church. But, like Anabaptists, they may be far more diverse in actual belief system than current historical knowledge may allow.
There was also that little matter of the Eastern/Western church split that shows a state of fragmentation which continues to this day.