Well, if there is going to be woodcutting and you allow to chop down trees, they must grow again somehow.
You can make them just \"respawn\" or make a system where the trees normally grow from seeds, get old, and fall down.
Registering each and every tree in PS would probably require much memory. Registering only the chopped-down trees and respawning them eventually is probably much easier.
Thinking of it a bit more, I find that the trees have to be kept somewhere anyway. If they can be cut down, they cannot be just part of the landscape. So they could grow in places which are considered good for growing trees, and are near other trees when nothing is in the way.
But if many people started cutting down trees there would be none left in a short time (assuming they grow for some 100 years at least - hundreds of in-game years is still a very long time). But there could be some \"fast growth\" spell (not neccessarily available to PCs), and some NPCs wandering around the cleared areas and casting it occasionally

Or woodcutters could contract mages to grow the trees for them

However, growing other things like mushrooms would get out of hand easily. There is a lot of space, mushrooms are small, and if mushrooms could grow virtually everywhere (or under trees), you would get zillions of mushrooms in no time.
But in reality there are sort of \"mushroom spots\" where they grow in plenty, and they are rare anywhere else. So it may not be to bad either.
Hmm, although farming may seem a bit different, the
farming thread is at least related. They think in there that growing everything everywhere is feasible, who knows.