> There's one significant thing they're achieving here: putting a price on CO2 in the atmosphere.
Just for fun: Humans have added ~1 trillion tonnes of CO2 to the atmosphere over 200 years, taking atmospheric CO2 from 275 to 407 ppm by volume. Ongoing emissions are around 36 billion tonnes (2015).
Climeworks apparently costs $600/tonne of CO2[1], with 10 year goal of $100/tonne (although skeptics estimate it really costs closer to $1,000, but I see no reason to believe them either). So the total cost would be $100 trillion to $1 quadrillion dollars to reverse climate change (this would be about a 50% overestimate since ~30% of emissions are anti-greenhouse aerosols), and the ongoing cost would be $3.6 trillion to $36 trillion. Over 80 years that would come to $4.85-$48.5 trillion annually, while the nominal GDP is currently just under $80 trillion. So 6% to 62% of annual GDP.
The total cost to transition the entire world to solar power including all heat, industrial and burning oil would be <$40 trillion, for reference. NB that's a very high level estimate with error ~= 50%
[1]: https://www.carbonbrief.org/swiss-company-hoping-capture-1-g...