I was just coming here to suggest a similar idea.
I found these two lines particularly interesting because I had a similar idea for how this could work. My thought with this would be that more advanced tools unlock more advanced recipes (still needing the saw to make planks, for example), but I was also thinking about the knapping system for this. Knapping is already a system for which you have to break away the parts you don't want, so a similar functionality could be used for wood. You chip off the voxels you don't want, and that forms the shape of the crafted item. That would also allow making things like the pan or the club to be a good way to pass the time early game, similar to making the clay items.
I like how part of it involved more firewood, and the ability to create sticks. This would be especially useful because those can be two very difficult resources to manage at times. I feel like this could be balanced by having you need to use the saw or something to get those increased recipes, that way the recipes are a reward for reaching the copper age. Early game logging, to avoid excess time, could be like real life firewood chopping where you wing the axed down on a chunk of wood to cut it in half, then quarters.
