Wow, that's an elegant solution. Just use wood, no problem. Well, there are a few....
Far long before the introduction of the steam engine, wood was extremely important because it was the only source of thermal energy available, besides the myriad of other uses it had. Subsequently, even before anyone would be in a position to try some sort of all-charcoal steam power scheme, Europe was on the way to deforestation. In some areas this was so acute that people would dry seaweed for fuel.
Now, before the industrial revolution there was a wealthy Netherlands which was a great manufacturing nation. The Dutch not only made glass, they also produced bricks, tiles, ceramics and clay pipes, they refined salt and sugar, bleached linen, boiled soap, brewed beer, distilled spirits and baked bread. All of that needed massive amounts of thermal energy. You can polish glass with a windmill, but you can't make glass with it. OTL, the Dutch were blessed with peat reserves which they could burn to accomplish that. If that peat didn't exist, couldn't they just use wood instead. Well, all of the forests in the region had long vanished by the 1600's. Couldn't they just make a deal with Scandinavia or something and import the wood, then? Well... no. It would simply have been exorbitantly expensive given the transport options available then. It was hard enough just moving peat from the mines in the north, getting wood from Scandinavia would be crazy. The same restrictions would no doubt be in place for an England without coal.
TLDR; It's one hell of a deterrent.