It would be impossible to grow trees in most true deserts, but in the Namib and Atacama there are places where sea mists roll in from the sea and condense on any object which protrudes from the sand. Maybe it's possible there. The most promising place for tree planting is in restoring the S.American rainforest, where there could be a huge environmental benefit. It could be financed with foreign aid money which wold go direct to impoverished rural communities, thus killing several birds with one stone.
There is a scheme underway in Britain to encourage the spread of sea grass meadows, which are important to the marine environment and apparently are more efficient at sequestering carbon than most things you can grow on land. Again the contribution will be small, but better than nothing. Sea grass is a true grass, but somehow manages to grow completely submerged in shallow salt water. Few people are aware of its existence. Restoring mangroves, which are basically small trees able to grow in tropical estuarine waters, is another area of environmental improvement which would also assist in the battle against CO2.
Burning wood instead of fossil fuels has a positive impact on the carbon budget where the carbon is recycled back into tree plantations.
Really, they are not the main actors on the picture: Oceans (38,400 Gt, lithosphere carbonates 60,000,000 Gt, lithosphere kerogen 15,000,000 Gt) but their cycles takes 100 years on the fastest one and hundreds of million years on the slower. But the fastest one is the biomass, and the most effective one is the tree. (Check Kiri tree)
The politics around these can get murky with respect to motivations ("why") but include both sincere efforts to make these work as one element of an emissions reduction policy - usually as a kind of stopgap action to give time for new investments in low emissions energy to flow through - as well as insincere efforts, to appear pro-active whilst not requiring substantive change to emitting industries. Or even to cash in on emissions reduction funding and/or funnel it inappropriately as political favors.
Because the climate issue had initially been widely framed as environmental and fringe rather than economic and mainstream it had been seen widely as driven by environmentalists who have long opposed land clearing and promoted re-forestation. Some of these schemes appear to have been developed by environmentalists and some to appease Environmentalists (and an increasing concerned public) who promote tree planting as a simple and environmentally beneficial act irrespective of climate change.
The climate problem has increasingly become seen as economic and mainstream over time and the effectiveness of reforestation as Carbon Offsets faces ongoing scrutiny, including by "green" political parties and others concerned with "greenwashing" (the contrived appearance of supporting emissions reductions goals whilst avoiding emissions reductions.