Large-scale tree planting can remove some CO2 from the atmosphere, but nowhere near as much as humans add by extracting and burning fossil fuels. See https://skepticalscience.com/1-trillion-trees-impact.html for a detailed assessment of what this looks like.
The IPCC has a chart showing what actions need to be taken over the next few years. Afforestation is one piece of many things, all of which we need to do.
Most trees are not expensive if you plant them from seed or buy them as a small sapling.
Source: I buy/grow a lot of trees and browse a lot of nurseries.
Sure. But whatever cost it is times a trillion is a lot, and there’s a multiplicative effect. The value of the trees will compound over time, and very likely private entities will be able to harvest those trees for sale. A non zero amount of any proceeds will eventually make their way into politicians’ donations.