Direct air capture is quite expensive, and also adds the question: if you can capture CO2 from air, why not just continue to use petroleum-based jet fuel and capture and sequester the CO2?
Objvious difference: no one who's calling the shots, is really worried about climate change or CO2. It's about switching away from non-renewable fuels to enable future economic growth. But because for leftists, "economic growth" sounds like "making the rich even richer" and switching away from non-renewable fuels threatens their sources of inspiration - Putin's Russia and Arab petrostates - they found a way to phrase the same in a manner the leftists will like "hey the Earth is burning, we need to do something about it!".
That's the response: doing as you suggest mitigates global warming, but does nothing to reduce consumption of fossil fuels, which is the actual half-hidden goal of all serious efforts to mitigate global warming. This is also why CCS went nowhere.