The technology is not at all questionable thermodynamically, because it has been working for billions of years in the form used by plants.
We are already able to do the conversion from solar light to electrical energy at better efficiency than the plants and sooner or later we should be able to reach similar efficiency with the plants at carbon dioxide reduction into hydrocarbons.
If someone will succeed to solve the difficulties of the direct electrolysis of CO2 or of carbonates, we may exceed the efficiency of the plants, which reduce CO2 indirectly, with hydrogen obtained by the photolysis of water.
The conversion of CO2 into hydrocarbons is precisely the only solution to the CO2 problem that cannot be questioned in any way, because it is the only solution about which it is known with certainty that it works, as anyone can see by just opening a window and looking outside.
Using energy from fossil fuels for carbon capture is so obviously absurd that nobody could do such a silly thing.
Normally any carbon capture installation must be powered by solar or wind energy, simultaneously solving the problem of the energy storage.