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Yep it would be better to at least have some trees that cannot be chopped down than to have none at all, even if it takes a long time to clear them all out. Eventually all trees will be gone unless the players make a conscious group decision to preserve some of them. As we've seen it's quite difficult to get much consensus on anything around here. ;-)
Why would you want to preserve some trees?Aesthetics?
I'd suggest and expect that in such a situation, the societies and or corporations would start to collaborate, and choose to hold territory and try to enforce no chopping of stumps. That kind of thing. Teamwork. Otherwise yeah, it could happen. Though if it would, i see no hardship in the way of the devs introducing new forests.The Allfather