Well again, I'm no official spokesperson. I speak from my own understanding and memory. When the ICOC was formed, we (I use the term loosely, because I was not a part of ICOC when it was first formed), wanted to accomplish something globally, which the mainline Church of Christ were not doing at the time. many main lines were invited to join the ICOC who shared the same vision, my congregation was amongst them. From my memory, the main lines disassociated themselves from the ICOC around that time. Over the years a new culture developed out of more radical convictions and we were no longer the same culturally as the mainline churches. When I speak of the mainline churches, I do not speak of one single entity. I am aware that there is a tremendous spectrum, with one end of the spectrum being very similar to us. There are sadly also some Churches of Christ which are dead in the water, stagnant, and even adopting baptist type salvation doctrines. If all manliness were one single culture, I think it would be easier, but they're not. The reconciliation definitely open the doors to reverse course and draw closer together, but we must also respect the differences. It will take time to work through things. Among such are, instrumental music. Some CoCs would be willing to worship with our instruments, and others would not. Some CoCs would join us in evangelistic work, others just want to maintain their status quo. My friend and I ran into a couple from a mainline CoC and we got along great, and wished each other the best. Complete unity is not done overnight. Changing the name would accomplish little.
Let me know if you need more.