This actually is the case. See Fossil Capital: The Rise of Steam Power and the Roots of Global Warming by Andreas Malm. I saw this argument featured in a video by "Our Changing Climate" that I can't seem to locate now. But I believe this book was the main source for the video. Coal never actually dropped in price during the industrial revolution. The new tech was just used to expand production. And it makes sense when you consider that for these industrialists, labor and equipment costs were probably a much bigger part of their budget than the bill from their coal supplier. Even today, with all our automation, labor remains the biggest expense of most businesses. And it's not like they just ran out of water mill capacity. They were still building dams in the UK well into the twentieth century. And ultimately, cheap urban labor combined with expensive coal power beat out expensive rural labor combined with cheap water power.

Water mills only produced a set amount of power that could be increased orders of magnitude by coal and steam.