this is an important part of the answer; the sheer quantity if timber which using wood-burning as an industrial power source requires. It simply isn't sustainable, especially in a world where transport was expensive and very limited in scope.
you have to consider that in the context also, of the huge quantities of timber employed in the old mines. How many trees were required to make a pump-rod, for example?
many years ago someone described coal to me as 'a forest worth of energy in a wheelbarrow' and I thought that was very much to the point
Very true, especially given that there was already significant demand for charcoal from the iron industry upping the price, and when you start factoring in the pressure of demands for timber for construction and wood for domestic fuel on the available forestry, coal starts looking much more attractive for running engines! Then take into account the greater heat for bulk ratio, plus the fact that most of the early engines were installed on coal mines or near to sources of coal and it makes sense to use coal in an engine, or for anywhere you need a lot of heat but sulphur in the fumes isn't going to be a problem for that matter....
As for other uses of wood in mines, stempling and shoring would certainly consume a great deal of hardwood poles, whilst pump rods most likely would have been made from imported timber. We've been importing large pine trees from the continent and the new world for a long time, and until the FC started growing it on a major scale, we didn't have an abundance of native product.
Follow the horses, Johnny my laddie, follow the horses canny lad-oh!