There is no problem.
If he were to design a system that generated energy without CO2 production and used that energy to remove CO2 from the atmosphere the total CO2 in the system would go down (the GP's desired outcome) while the output of energy at a distant coal plant would remain unchanged (no thermodynamic issues.)
What energy source could he use? Well, plants figured out they could use the sun to fix atmospheric carbon into solid forms (polysaccharides) and somehow thermodynamics never crapped out as a consequence. The GP never said the energy created by the coal plant would be used to remove CO2, you did. You are projecting your short-sighted myopia and being pointlessly critical of an effective idea.
If we accept that the currently most worrying pollutant coming from hydrocarbons is CO2 and we further accept that solar energy suffers from logistic considerations that prevent solar energy's wide-spread implementation (not my opinion but accepted for purposes of discussion) we can still use that solar energy to mitigate the negative effects of hydrocarbon based energy production (CO2 emissions) while leaving the benefits of hydrocarbons (portability and on demand power) intact.
Try to use that beautiful brain of yours to come up with solutions.