"The center is in Rome.
No other core exists, as none of the 27,000 groups thinks having such a core is necessary.
"
That is, of course, the RCC's position, and it's one that can be defended, too. However, there are other large denominations that have core beliefs as well, so you're incorrect on that count, I'm afraid.
Still, the continuing splintering of the non-Roman Catholic Christian Church (I recognize the Eastern Rite Churches, as well, as being of the ancient core) is troublesome for Christianity, in my opinion.
I see folks discussing doctrine with regard to these small, independent churches, yet, when I talk to folks who either lead or are members of these small churches, I find that they are referring, usually, to very small aspects of doctrinal difference to justify their separation from others.
Between the RCC and Martin Luther, the differences, doctrinally, were really actually pretty minor, and had to do primarily with intercessionary stuff.
Still, if you attend, say, an Easter Sunday service in a traditional Lutheran Church, then go to a Roman Catholic Church for Easter Mass, you'll be hard pressed to find much difference in the two.
Christianity seems, with some exceptions, to be fragmenting, and I don't think that's a good thing. Even the Roman Catholic Church is in danger of fragmentation, I think, right now, with the American Church pushing hard at some basic doctrinal issues.
Read the 95 Theses and Luther's selected works. The differences were not minor, as you say, but significant enough for him be excommunicated. He disagreed with the concept of the Mass as Sacrifice, the Pope's power of the keys, Transubstantiation, priestly celebacy, and the 7 sacraments--I think he whittled it down to two--baptism and communion, if memory serves correctly; he certainly thought it less than 7.