This is literally[1] burning $300,000 to save $100. No matter how well you optimise that $300K, it will never ever EVER be less than $100. It can't possibly be, that would break the laws of physics and you'd have essentially a perpetual motion (free energy) machine.
If you have 'x' units of carbon (coal), which you burn to make 'e(x)' units of energy and some CO2, turning the resulting CO2 back into 'x' units of carbon will always take more than 'e(x)' units of energy. There is no magical future science that can enable this. It's a fundamental law of thermodynamics!
If it were possible, then you could turn 'x' units of carbon back into 'x' units of carbon PLUS have some free energy left over by running the above in a loop. That's absurd. That's literally a perpetual motion machine. You could start with one ton of carbon and never need more to make infinite energy.
There is an endless series of "science" papers like this published every year, because it gets funding and attention from people that just don't understand that "there ain't no such thing as a free lunch". They're a total waste of time, and have the same logic as trying to power your ceiling lights by using solar cells as your wallpaper and then connecting the lights to the wallpaper. Isn't that brilliant!? The photons from the ceiling lights will produce electricity in the solar cells, which in turn will power your lights! Never pay electricity bills ever again!
NOTE: There are ways of capturing (not "un-burning"!) carbon dioxide and trapping it for less energy that was released by burning the carbon that went into it. That's fundamentally different, and potentially economically viable.
[1] Literally! Not figuratively! This process literally burns expensive gallium metal to produce cheap carbon and burnt gallium (gallium oxide).