throw in some water and make sugars. About the same idea as photosynthesis. Of course, electricity-driven reactions don't tend to be all that controlled and there is a lot of competition by other reactions, so costly and inefficient is probably a good description. It is why we don't already do that.

Just making carbon would be a fool's game, because the carbon would want to react back with any free oxygen as soon as it could. generally as a big fire. Sure, we can deal with elemental carbon in lots of ways (it doesn't generally spontaneously combust) but you would have to do something with all that carbon. And, of course, there is the question of how you make the electricity in the first place, ideally not from burning coal or inefficiencies would mean you release more CO2 than you break apart/recover.

But yeah, at least it is an idea. Thinking and coming up with ideas is usually a good thing. Most ideas turn out to have more problems than they solve, but occasionally a good one comes up, so don't stop, don't get discouraged that your idea isn't practical. Hardly alone with that.