So to run a DAC plant from a grid that has a decent proportion of electricity generation from fossil fuels, you are making it worse overall (producing more carbon to power the plant than it is removing), and conversely, if you are running a DAC plant from 100% clean energy, you'd get better bang for your buck if you used that clean energy to displace fossil fuel use (because every kilowatt hour of fossil fuel energy you can replace with clean energy prevents a larger amount of carbon being emitted than the DAC plant could remove with the same amount of energy).
From a thermodynamic point of view would only make sense to run a DAC plant somewhere that already had a 100% clean grid, and only when it happened to be producing a surplus of clean energy.
Any coal plant - carbon capture plant combination that captures more than it emits would easily be a perpetuum mobile.