probably wood is not strong enough nor not dimensionally stable enough for most applications. Nor can it resist the high temperatures in most applications.
If you are talking about the piston in an internal combustion engine, probably it can't be of wood. The temperature inside the engine will be very high and the wood will burn. Piston needs to be of metal only since its friction is very less. Engine oil can't be added to wood because wood becomes soft if you add oil to reduce the friction. Wood fails here. It doesn't have that much strength also to push the wheel, it will break.
Don't think that's possible since the maximum temperature inside will be close to some 5000°C, the wood will burn.
Maybe, if of a very hard wood for use in something like a hand operated water pump/syphon.
