CO2 is a trace gas in the atmosphere, to begin with. Less than 1% of the atmosphere is CO2. The amounts involved are incapable of causing the scaremonger climate predictions. This is something the modelers themselves are forced to acknowledge, and sends them searching for unknown "amplifiers" in the climatic system, which they have no reason to suppose exist. They simply try to justify past predictions whose scale has been shown to be off by an order of magnitude.
Yes, vegetation traps carbon. It takes an increase in overall biomass to do so. Forest grows such additional biomass on its own, to limits set mostly by available sunlight on the one hand, and available soil nutrients on the other (especially "fixed", rather than gaseous, nitrogen). When trees die and fall down and decompose, they are converted back. Fungi and insects eat them, become food for other animals, which exhale CO2, etc.
If it every become truly necessary to sequester carbon for long periods, it would be simple enough to do. You'd just purposefully fertilize mid ocean algae beds in temporary "algae blooms", which after a brief cycle die and sink to deep ocean floors. Trapping carbon there. This could be down well away from prime fishing grounds to avoid disruption of their ecosytems, and the locations varied from time to time. No one will ever run out of ocean floor, or algae. Some algae varieties can be fertilized with milled iron filings (dissolved iron makes their oxygen transfer process more efficient) - "rust" is hardly scarce.
Not that there is any need to do such things at present. The entire scaremonger industry around the subject is a boondoogle from begining to end.