Sweet
This only ignores a tiny issue with the CO2 capturing part (that is why we're doing this, right?)
The CO2 in our atmosphere is there because we took energy out of a system, with CO2 as a by product. If we want to convert that CO2 back again to carbon, plastics, you name it, we will have to put back that energy we took as well.
We've been doing this CO2 dumping for a good two centuries now, and we're still at it. The atmosphere has a huge amount of extra CO2 because of that, and if we want to air out all that CO2, well basically have to spent give-or-take the same amount of energy that we've been taking for the past two centuries.
If, starting tomorrow, we magically use only solar, wind and nuclear, and we magically double our energy output, we would have to spend about 50% of our entire energy budget for the next century to pull out all the excess CO2 from the atmosphere. This is ignoring the storage problem (where to safely store it, stable, how, and conversion to anything that can be stored will require energy too) and ignoring things like energy conversion efficiency and losses that typically is around the 30% or so for most engines, meaning that in reality we might actually have to spend multiple centuries on this.
No matter what we do, this is not a problem that anyone alive today will see fixed. This problem is humongous, if not humanity ending, and yet somehow most people think it's something science will solve within the next few years.