One of the greatest thing about this game is the the fact that it is simple, light weight in terms of cpu processing, and fun for all ages. I think if these kinds of things are added to it, you will get away from the fundamentals of the game in the first place. You will bring complexity, more cpu intensive, and although rpg's are fun and addictive not everyone is into them.

I agree that half cut trees suck. But i do think that cutting down a tree with one chop or reducing the effort required to get the wood from it takes the challenge away. I'm thinking you could go two ways with this. You could either create an invention that you have to build like a robo saw that you set on the trunk and it takes a bit but it ultimately after a timer ends and it chews through the wood the wood blocks and saw drop down to be picked back up. Or another way to deter half chopping is to have a plug in or something which basically would put a 10x10 trigger around the person once the first wood would be chopped. If the character passes this trigger without all the tree block removed from that particular tree then the wood gets removed from your inventory and put back on the tree.