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Making this work is all about minimizing the energy (and thus economic) cost of this first step. Then you need to reduce (add hydrogen and remove oxygen) the CO2 and start building other products - methanol, long-chain hydrocarbons, etc. (that's shipping and jet/rocket fuel, respectively). But why stop there? If you want long-term stable materials, converting the CO2 into carbon fiber is a good option - more sci-fi is a diamond endpoint, which takes a lot of energy, but has many uses.
This will have minimal effect on atmospheric CO2 unless fossil fuel extraction and combustion is eliminated from the energy mix - but it does point to how human civilization can do material and fuel production without having to mine carbon from the earth or cut down forests. In the long run, this is the only plausible option.
Out of the 27 commercially operational CCS projects worldwide, 21 inject carbon dioxide into oil reservoirs to force out petroleum: https://www.landclimate.org/what-is-happening-with-carbon-ca...
While renewables capture an inexhaustible source of energy (Sun), fossil fuels rely on an inexhaustible source of money for them: subsidies. Fossil fuel companies can't survive without the hundreds of billions of subsidies every year[1]. They can capture more subsides for 'carbon capture', using the captured carbon to extract more oil.
Exxon bets carbon will be the new oil: https://www.semafor.com/article/07/21/2023/exxon-carbon-denb...
[1]Global Fossil Fuel Subsidies Reached $7 Trillion in 2022, an All-Time High: https://e360.yale.edu/digest/fossil-fuel-subsidies-2022