It’s not so much that it doesn’t solve the problem as things just don’t work that way. For starters, current energy distribution methods are local monopolies, so they are strongly regulated on price because the competition mechanism doesn’t work as it should. The idea that a customers might “choose” cleaner energy doesn’t always work.
Also, to a great extent, electricity is fungible. Suppose you have both windmills and coal-fired plants connected to the same electrical grid, and they both generate equal amounts of power. Now suppose I tell the electric company that I only want to buy power from the windmills, so instead of getting half wind power and half coal power, I get 100% wind power (on paper). However, the electric company doesn’t actually have to change the way it produces electricity in order to do this. All they have to do slightly increase the percentage of coal power that they deliver to everyone else (on paper). So all that changes is numbers on paper, and there’s exactly as much coal power being generated as before.
Also, to a great extent, electricity is fungible. Suppose you have both windmills and coal-fired plants connected to the same electrical grid, and they both generate equal amounts of power. Now suppose I tell the electric company that I only want to buy power from the windmills, so instead of getting half wind power and half coal power, I get 100% wind power (on paper). However, the electric company doesn’t actually have to change the way it produces electricity in order to do this. All they have to do slightly increase the percentage of coal power that they deliver to everyone else (on paper). So all that changes is numbers on paper, and there’s exactly as much coal power being generated as before.