Thus wouldn’t it be feasible to push that energy back in or back out using methods that may use the same amount of energy, though yield far greater results?

Yes, it’s possible to improve efficiency, up to a limit set by thermodynamics. In this video, a scientist (granted, astrophysicist) talks about it: https://www.youtube.com/watch?v=EBN9JeX3iDs

Even if we built a 100% efficiency direct air capture system (which is impossible) to get down to 450 PPM CO2 levels by 2050, which is frankly too much already, and even in the more optimistic emission scenario – all of that still demands roughly 5% of the planet’s entire electricity production to be diverted to these machines.

While capture is necessary, it will physically not suffice. We have to stop emitting more; keep fossil fuels in the ground.