Coal wouldn't disappear overnight even if a tax made it uncompetitive with other sources of electricity. There's a ton of infrastructure that would keep it going for quite a while. That's why I can't reconcile "today, absent coal" with this idea.

Anyway, to your point, I think there must be better ways to help poor people afford energy than to subsidize the electricity of wealthy people and industries. Set aside a small portion of the tax revenues for helping poor people pay for electricity. The important thing with taxing an externality is to capture the cost, what you do with the money matters much less.