So basically: this is nice, but there's no reason yet to think that this could be the way we slurp carbon out of the atmosphere and avert climate catastrophe. Right? Drat.
Well we already have a solution for that. We just need to create massive farms on unused land. Plant enough stuff to feed the world populations of humans with large excess and you're going to also plant enough things to scrub co2 out of the atmosphere.
Just curious, but my understanding is that plants are generally carbon neutral. Any CO2 that is taken in by a plant is eventually broken back down and released after the plant dies and is consumed or allowed to decay. Unless you take a significant amount of that plant matter and contain it so that the carbon can't be re-released, at best you get a static reduction of CO2 directly proportional to the increase in live plant volume.
So, no carbon scrubbing while feeding the world, but you could maybe scrub carbon by taking massive amounts of excess crops and burying/sealing them away. Not sure what the cost/efficiency of that would be.
You are correct: To get a net reduction of atmospheric carbon dioxide, you need to increase total plant mass or prevent plants from decomposing/being eaten.
As far as I know, the majority of net oxygen production happens through algae, because they die and sink to the bottom of the ocean, permanently removing carbon from the carbon cycle.