It's an easy way to get a patch to complete a quest or to get an achievement for planting beans. If you want to have a wood tree, your home is the safest place.
I've been nurturing our neighbourhood tree for ages, but I have to confess I've harvested it and cleared it myself, by accident, not just once but twice - all it takes is an accidental second tap on return if you think you're gonna water/pet it, but someone else has already done that recently. I can see how a newish player isn't necessarily gonna have the currants to re-plant if they do that.
I think it's a pity they're so fragile and there are virtually none anywhere outside the quarters any more - the rarer they get, the more likely the remaining ones are to exist perpetually as stumps, constantly at risk of accidental harvesting-and-clearing. I'd like to see a few wood-only plots *somewhere*, I think, perhaps in one of the public gardens?