But it's not just a matter of agreeing with this in principle as a description of general historical processes. The phases of your empire will have names that have RL associations, and the sequence will be discordant against those associations. One can agree with the proposition that that "civilizations are a set of ideas that morph with time . . ." and know that Rome doesn't evolve to Mongolia. To experience it your way, a player will have to ignore the specifics of the second civ and just think of it as Generic Second Civ built on the ruins of my First Civ. But civs' specifics are a big part of how they are defined and a big part of what gives them appeal.
This is what a good early post on the matter argued (I wish I'd taken better note of it): When you're Egypt and you shift to Mongolia b/c you have three horse, don't think of yourself as Mongolia, think of yourself as Horse Civ, or Egypt in its Horse Civ stage. But unless renaming is allowed, the screen is going to read Mongolia.