Geology tends to have two schools of thought: Uniformitarianism and catastrophism. Both processes are evident. Neither affords the certitude we would like to have when attempting to understand its entire history. The stark delineations in the diagram you posted I tend to attribute to catastrophic processes. Almost all of the fossil record I would also attribute to catastrophic processes. Can you prove me wrong? No. But you can offer up some reasonable scenarios to counter my own understanding.
We aren't still arguing some of the things you think we are. In other news, phlogiston theory is dead.