(Burning methane is even better as it releases much more energy per unit CO2 i.e. ~860kJ-per-mole-of-CO2 vs anthracite's ~400kJ.)
And as others have said, rocks actually are able to exothermally absorb CO2 permanently. It's possible to speed this up by grinding rocks to a powder, placing in water with a catalyst.
...none of this is to say I support relying on direct air capture and just go ahead and burn fossil fuels. We need to keep that in the ground and transfer the whole civilization to non-fossil fuels, otherwise if some populist jerks wer elected, they could just order the expensive direct air capture program to stop (can't do that if you're already transitioned to clean energy and all your wellheads and drills and coal mining equipment are rusted or melted down for scrap).
Source: [0] https://www.researchgate.net/publication/257177020_The_therm...