I ask this out of ignorance: How is coal heavily subsidized? Do you mean it's subsidized because they're not being charged for the emissions that they generate?
Coal power was probably a net benefit in the beginning, but there are much better alternatives now.
One way they do this is Percentage Depletion. A mine take out 10% of the available coal, they can deduct 10% of the value of the mine, to the point where the total deductions can exceed capital costs.
There is also deduction that came about because they wanted to promote domestic energy production and reduce dependence on foreign energy fuel, which between the year 2002-2010 awarded $12.2 billion in tax credit to coal alone.
The Wikipedia page has a nice breakdown: https://en.wikipedia.org/wiki/Energy_subsidy