It's more complicated than that. Yes, not all the land was being actively maintained at any one time but the 200ft pines, abundance of fruit/nut bearing plants and game species that come with them is a direct result of native land management practices throughout the broader region despite any particular square not necessarily being actively managed at any particular point in time.
Relocating (and they didn't relocate far, remember this is inhabited land after all, you can't just set up shop on the neighbor gang's turf) is the native equivalent of leaving a field fallow. But because the natives were working with animal and plant species the feedback loop is potentially decades long (depending on local resources) vs farmers who will leave a field fallow every few years.
I agree that they would have left the place barren had they had the means but you have to consider that what they were doing was stable on a 500+yr timeline which is a pretty good run.
My point here is that the impenetrable thicket a lot of environmentalists want to maintain is not particularly representative of "peak forest". I'm sure they all want to see blueberries and 200ft pines but just doing nothing won't achieve that because that's not a state that new england forests can (and certainly not today since we've got all sorts of invasive species and pests) get themselves into without human intervention either directly on a particular parcel of land or on enough near proximity land to influence the ecology of the parcel in question.