Sometimes the labels we place on things create more weight than need be or add unnecessary confusion. There might be a bit of that going on here. After Jesus died, let's say in the year 50 or 60 for example, any new Christian with a heavenly hope would have to have some recognition of the apostles. They were the ones that traveled with Jesus, recorded the events and his words. If you were a new Christian at that time, unless you had a unique privilege of spending time with any of the original 11, likely much of your knowledge came from 3rd or 4th hand word of mouth and/or the writings circulating at the time. When circumcision became an issue and Jesus wasn't there to answer it, it fell back to the group with the best credentials to answer the question. Everyone seemed to recognize that as appropriate. There might have been a few dissenters still but they didn't make it into the Bible and memory of them has faded.
When Brother Knorr proposed Gilead some of the brothers gave him a hard time, 'have you no faith' they were reported to have said meaning if you really believe Armageddon is coming why are you getting involved in all this. Some people when they grasped the size and length of the work Gilead would begin (beyond many observer's lifetimes) concluded this is God's work, not mans. I find the lower case gb for the first century governing body and the switch to capital GB for the modern day very peculiar. Still, there are tens of thousands of congregations around the world that can trace their existence back to what Brother Knorr started. That the current GB has inherited that organization does give them some claim. Jesus is still the name that saves but they have inherited the vast delivery system regardless of if the Kingdom is officially ruling yet or not.
I was at the annual meeting for the talk that later became the article 'The Faithful Slave and its Governing Body'. This was the precursor to the talk and article confining the FDS to the responsible brothers at headquarters. (and that talk was not a change, it just used new words to describe what was already in place) I was told at the time the reason for the talk was that there were many younger anointed from democratic countries that felt they should have some say in what the organization was doing. Setting aside the issue of when the slave is found faithful and discreet, I do agree there is a negative aspect of too many cooks in the kitchen. It does not matter if we drive on the left or right side of the road, it matters that everyone drives on the same side.
Everybody thinks that the Bible does not tell us when the end comes. It tells us exactly when the end comes. When the number is filled. I do not think it had nefarious intent, but considering what was taught and believed at the time, I can thoroughly understand why the brothers thought the heavenly call closed in 1935. But if it was not true, even if reasonable for the circumstances, it was almost an anti-Christ like teaching. It might remind some people of 'you shut up the kingdom of God and prevent others from going in'. Regardless, that teaching never stopped Jehovah from anointing who he wanted and it eventually fell by the wayside. I never believed resurrected ones wouldn't marry and that teaching fell albeit a bit dysfunctionally.
I disagree with your last sentence above, history proves they are unable to mediate the new covenant, they tried to shut it up, declare it closed, even if it was done innocently and with good intent, it was unable to stand because they are not mediating it. You just agreed that the group isn't positively identified until the end so how does that really translate that someone can't be anointed without recognizing them as the faithful slave. This is where those labels get tricky. It might be more accurate to say it is not possible for someone to be anointed without much of the information they have made possible, just as in the middle first century it could not happen without the knowledge the apostles made available. Even Cornelius had to be baptized in Jesus name after receiving the Holy Spirit.
I thought it very insightful on your part to to think they should not be part of a legal corporation when they had already separated. It is very unusual for someone to be thinking about those things.