If you chemically try to, you have to avoid combusting the coal or putting it into a form that isn't combustible or through a process that lowers its potential

If you chemically try to, you have to avoid combusting the coal or putting it into a form that isn't combustible or through a process that lowers its potential chemical energy in the powerplant. That leaves physically, which is really tough considering that it would probably require a chemical transformation to be able to run it through a centrifuge (like uranium gas in uranium centrifuges) in order to do the separation, and centrifuges can require nontrivial amounts of power to run, so no free win here either. On top of all that, now an output is a more-concentrated radioactive material (a lump of uranium), and suddenly whoever is doing this removal has quite a number of new NRC and OSHA regulations to follow, which are known to not be economically cheap. So it's no wonder businesses default to "just burn it, let the public suffer the externality costs". Edit: To be fair, a variant of this this has been attempted before: see the gasification of coal and the "clean coal" movement. It failed.