The first one requires development, construction, installation and maintenance of equipment; it requires explicit effort from many people; it will need to be decommissioned at some point; the storage will have some marginal cost (e.g. containers, drilling holes, etc. depending on the method). These things all cost CO2, unless the economy has already been decarbonised (in which case it wouldn't be needed).
More importantly, being "free in terms of CO2" is still an all-else-being-equal perspective. It's focusing on one aspect (CO2 emissions) of one small cog (a CO2 extraction+storage plant). If we look more broadly, each barrel extracted is offsetting less than one barrel being burned elsewhere (since nothing is 100% efficient). CO2 extraction and sequestration is thus a form of power transmission: the work that is required to offset emissions (e.g. from a car) is being performed away from where the emissions are made (although for flue capture this might be quite close!). For example, we can think of these as being roughly equivalent:
- A fossil fuel car with solar-powered carbon capture and storage onboard
- A fossil fuel car with solar-powered carbon capture and storage in some other location
- A solar-charged battery-electric car (+ a little CCS to offset manufacturing emmissions, etc.)
These are all solar powered and carbon-neutral (as long as they offset enough). Let's say they each receive a similar amount of solar energy: the first will not get very far, since offsetting is very energy intensive and it needs more fuel to carry the solar+CCS equipment. The second is more efficient, since the fuel doesn't need to move the solar+CCS equipment; it's as if the offboard CCS is transmitting a little extra power to the car. The third will get much further, since the battery and electric motor make much better use of the solar power than the CCS system.
The first approach is clearly silly. The second is useful in situations where renewables can't be used directly (e.g. jumbo jet fuel), but is incredibly wasteful and expensive compared to the third. The third approach is best, and should be used as much as possible.
If somewhere has an abundance of renewable power (e.g. geothermal in Iceland), then "transmitting" it elsewhere via CCS is much less efficient than, say, laying a high-voltage DC line; or moving high-energy, location-agnostic activities to the region like aluminium smelting or datacenters.