For example, the calculation above shows globally removing our current rate of CO2 production using one of the more expensive technologies behind this service would still be only about half as expensive as WWII was for the USA in terms of fraction of GDP. Expensive, sure, but clearly not impossible. If we were really "at war" with the climate change problem, it would be still cheaper than an actual war.
Except that it is not just about money. Say you invent a machine that takes CO2 out of the atmosphere. How do you build it? With energy, and in the foreseeable future, out of mostly fossil energy, which emits CO2 (you need machines to extract the material needed for that thing, machines to transform those, trucks to move everything around, energy to make the machine run, energy to maintain it, etc). So you emit CO2 to create, run and maintain a machine that will try to pull it out of the atmosphere.
> It’s fine to emit a small amount of co2 to extract a larger amount.
No it is not.
Simple example: if you need 1000 times the remaining fossil fuel on Earth to extract the CO2 needed to "save the climate", then by definition you simply don't have remotely enough energy on Earth to do it, so your system is not only not viable, but it's counter-productive because it is using some of that remaining fossil fuel for almost nothing.
