Perhaps globally, but regionally, you're flatly wrong in at least two ways: First, on a regional level, civilizations could heavily deforest their surrounding

Perhaps globally, but regionally, you're flatly wrong in at least two ways: First, on a regional level, civilizations could heavily deforest their surrounding ecosystem to the point of devastating it and themselves with long-term consequences. A couple examples are the Romans, pre-modern Britain and of course, the Maya. Secondly, the productive practices of pre-modern times were far less efficient in many ways than they are today, meaning not only heavy dependence on forest or at least wood resources, but also a much more impactful destruction of forest land for needs that in many societies today are handled without resotrting to wood.