Which makes it obvious that the entire idea is pretty pointless, burn fossil fuels to generate energy to then use it to unburn fossil fuels. To do it with renewable energy, we still need the same capacity as the fossil fuel capacity and when we have that - ignoring issues like fluctuations in renewable sources - it makes more sense to just use the renewable sources directly instead of using them to undo burning fossil fuels.
If you want to use the process to pull carbon out of the atmosphere, then you first have to replace all fossil fuels with renewable ones, then you can use additional renewable capacity to remove carbon. Add additional 10 % capacity to the world energy capacity to undo one year of carbon emissions every decade, at least to a first approximation.
To come back to the initial question, you essentially need an industry the same order of magnitude as the fossil fuel industry to have a meaningful impact. Not going to happen anytime soon.
This would true if we need to re-create the original molecule with it's stored energy (plus losses of course).
However, it seems this is a misapprehension of the task. Instead of trying to recover the entire hydrocarbon molecule, we're "just" trying to extract or recombine the CO2 reactant.
Without doing the chemistry or the math, it seems likely that a variety of methods of either preferentially attracting CO2, or combining it into simpler lower-energy-dense molecules to be collected, would require less energy as was in the original hydrocarbon, often substantially less.
Seems it should be an inequality, not an equality. Or am I missing something?
If you capture the carbon dioxide, then for every supertanker full of oil you burn you need to permanently get rid of a supertanker full of liquid carbon dioxide. This is of course a project of insane scope given that we burn billions of tons every year. So in order to not have to deal with the waste, what if we just turn it into something useful that people will pay for? Because that costs a lot of energy, the energy we just extract. And now you want to put it back in? To get back what you just burned or at least something similar that you could almost certainly produce more efficiently directly from the oil?
That said, it still seems an extremely useful measure, even if we keep using only single-digit percentages for long-use plastics instead of hydrocarbon fuels.
Let's assume that for the next century or so a bunch of applications will continue to require the convenience and energy-density of liquid hydrocarbons. In order to avoid extracting more and further increasing CO2 levels, we'll have to input significant energy to reconstitute them from CO2. Obviously, inputting that energy from more fossil fuels defeats the purpose, but using renewables will work; and now they are even cheaper energy inputs.
The result would be a cycle of newly fabricated hydrocarbon fuels, which can be custom-optimised for each application. No new CO2 would enter the atmosphere and the existing levels would be reduced by the amount of hydrocarbon fuels (and plastics, etc.) fabricated and in existence throughout the entire chain of existence, fabrication, storage, distribution, transport, in-vehicle, right up to the moment it is burned. With cheaper renewable energy inputs and optimized custom fabrication, it would likely get cheaper than the existing drill/pump/transport/refine process. And, it's permanently sustainable, and as liquid hydrocarbon fuel use declines, custom production can be converted to storable materials.