We could. It would be horribly inefficient, taking way more than other methods, and most importantly, the current methods of power generation would produce way more CO2 than this destroys. And to make it work at all you would need to remove the CO2 from air to get a tank full of it; at which point you could just sequester it, store it underground, or whatever else works and takes much less energy.

Both carbon and oxygen are way easier to get differently, even if energy were free it would not be worth it.