And what's wrong with that? Who says the coal has to be a net source of power?

Synthetic fuels are actually a pretty viable method of decarbonizing, especially for hard-to-decarbonize applications like aviation. Sure, you don't get net energy out of them, but who cares? Thanks to dirt cheap solar, our civilization has stupidly abundant access to energy. It's only portable energy or energy when we want it that costs a lot. But people have seriously proposed making even gasoline from atmospherically derived carbon. Sure, it's just a fancy battery. But the Joules/dollar you get from the grid is so much cheaper than what you get from gasoline that it may be worth it.