During the "most recent common ancestor" period, as you said, there's a single individual who acts as a common ancestor to all those alive today. Let's for sake

During the "most recent common ancestor" period, as you said, there's a single individual who acts as a common ancestor to all those alive today. Let's for sake of argument say that person is Genghis Khan, that Genghis Khan is somewhere in every current living person's family tree. How about Genghis's parents? Mr. and Ms. Khan (actually Yesugei and Hoelun) are surely BOTH common ancestors to everyone alive today. And surely Grandpappy Khan and the other three grandparents, and so on, going back. That ancestral tree keeps growing and eventually, you'll get to the point in the past that everyone alive at that period is an ancestor to Genghis Khan. Which means they are all also in our family tree. Therefore we all have an identical looking family tree from that point backwards.