This thing is not not really useful for climate change, instead it can provide CO2 gas we already concentrate for producing dry ice etc.
Incidentally, it is my understanding that coal use is already declining rapidly. In many cases, it is being replaced by natural gas: certainly not ideal, but better.
Early studies suggest that diverse silvopasture can be just as productive as monocropped grain, but it means a major change in diets and the food production system world wide. It means less meat (but not no meat) and a diet focused more heavily on fruit and nuts rather than grains. This is a huge cultural shift and also a huge economic one, since much of the food industry is completely dependent on value added processed grains.
But if we start looking at how chesnuts, hazelnuts, walnuts, and acorns could be stored and processed into a greater variety of foods, then we can start the move towards agricultures that are just as productive and way healthier for the environment.
No-till, poly cropped grain production (corn, beans, and squash in the same field) can also act as a carbon sink, but it doesn't lend itself to mechanized harvest right now, so it would need to happen to a smaller degree.
Based on your usage of "much" in this sentence and then detailed plans around crops, there must be some studies that quantify this to some degree. However, in my searching, I haven't found any such studies. Do you happen to have any favorites? Perhaps I need to dig into some of the IPCC references on land usage next.
Which basically means it's not going to happen. There are lots of ways to fix climate change that involve large scale changes to human behavior and habits. They're not viable because nobody is going to do them. The reason devices like this are valuable is that they promise to allow us to keep doing the things we're doing and stop or slow down climate change.
At a rough estimate it takes about as much energy to pull CO2 from the air as you get from burning it in the first place. So, your also mining coal, building a power plant to run an extractor for ~zero net gain.
And even if not, and even if it only made sense with a clean-energy input, you would still only need to power that one engineering project's infra with the clean energy, which is much more feasible than replacing the entire world's infra.
A one-time giant solar array with CO2 condenser is still easier than all the infra swapout (which has its own CO2 costs) and international coordination necessary to end CO2 emissions.
Coal power plants which have much higher than normal CO2 concentrations in their smokestacks have looked into carbon capture and they can't pull it off without killing their power output.
Now, if we limit Fossil fuels to say Aircraft and Boats then we already solved the problem because their are a lot of natural and man made carbon sinks like your local dump. They are not enough simply because of the scale of fossil fuel usage.
The economics tell us that we need to continue to burn things. At the same time collection will get better. Hopefully the one will go down and the other up. I for one am hopeful about this.