Interestingly, this isn't true of prairie grasses - their root structures can go several feet deep and make up most of the biomass of the plant. They're really underrated with regard to how much structure they make.
We are sending M. Sativa (alfalfa, lucerne) into space this October in our 10th plant mission in microgravity under a global education project with UN and others called “carbon farmer”.
Stressors in microgravity could shed clues on optimization for a changing climate and off-world production.
Post flight research (tomography, electron microscopy, single cell transcriptomics) is being done at Lawrence Berkeley National Lab and the Joint Genomics Institute. HTTPS://magnitude.io
Trees don't absorb any more sunlight than an equivalent area of grassland, so I'd be surprised if mature woods sequestered any more CO₂ than grasslands did.