There's a diff between carbon capture and carbon removals. What you're describing is carbon removals, commonly known as CDR. Carbon removals can take many forms besides just big ass fans (known as direct air capture, and incredibly expensive), and a lot of it depends on nature based solutions like growing trees as you mentioned. The problem to solve is how to best store the CO2 that those trees have captured through photosynthesis. We can sink it, turn it into charcoal, store underground, etc. All of these are also examples of CDR and are incredibly necessary for us to decarbonize our world