Imagine that you have a fire in a fireplace. You've expended j₁ joules of energy moving that firewood into your house, setting it up correctly, and igniting it.

Now, you've got another fire, using the exact same amount of wood, in the forest under a tree. The wood happens to have been piled up perfectly to ignite, and--oh, look at that, a squirrel brought an ember over, igniting that fire. You've expended j₂ joules of energy starting the outside fire, and j₂ = 0.

Ok, let both of the fires burn out. Now let's clean up the ashes, and we'll call the amount of energy required to do that c₁ and c₂. Assuming that you're moving the ashes the same distance to dispose of them, c₁ and c₂ are equal; in any case, any difference is completely unrelated to j₁ and j₂.

Carbon capture isn't trying to rebind the molecules or anything. It's just trying to vacuum up the carbon and sequester it. In fact, plants already do carbon capture really, really well, and they certainly don't require a ton of energy to do it. Amine scrubbing (an ~100 year old technology) is used to capture carbon from power plant exhaust, and it's using 0.11 mWh to scrub about one metric ton of carbon; but to create that much carbon the plant produced about ten times as much electricity.

Now, does any of this mean that carbon capture should be the first step? No! The cost is currently huge; something like $50 per ton removed, and that's even before you consider how you're going to get all the air through the amine scrubber. It's definitely more cost-effective to switch to renewables, reduce usage, etc. But the time will probably come (and honestly might already be here) where that's just not enough. When that happens, we don't need to worry about doubling our total output; increasing it by 10% or so should do it, and if we're really good at usage reduction, we can probably divert some of that saved energy toward capture.