Right now most of CF is produced with PAN (Polyacrylonitrile) Polymer. Which is commonly referred to as Acrylic fibers. These are produced with feedstock of Petroleum. To oversimplify how we go from PAN to CF in the process is just usage of alot of energy to kick out Hydrogen and Nitrogen from PAN polymer chains resulting in long chains of pure carbon backbone or Carbon Fibers.
This is a really good alternative usage of Petroleum outside of it's use as a fuel. In future when most energy is coming from alternative means (solar, wind, geothermal etc) that Petroleum would be utilized to manufacture products such as CF among others. The prices of Petroleum will go further down when it's primary market of energy generation and powering vehicles keep going down. Therefore, the feedstock for CF would be significantly cheaper and instead of burning Petroleum products into CO2 we get to utilize that Carbon into making cars, furniture, aircrafts and other thousands of objects.
Going the way of plants to get Carbon is just going to make worst impact on environment as more area would be required to breed plants that yield high Carbon content.