But if you harvest biomass at anything like that sort of rate, the ecosystem collapses fairly rapidly. You need to recycle a lot of it in order to preserve soil fertility, and leave lots more of it in place to stop the soil from eroding. Take too much and you end up with the Oklahoma dustbowl, but on a global scale, and with nowhere else to migrate to.
We're already harvesting a great deal of that (municipal green waste, etc.) but not using it effectively.  Further, a lot of what isn't technically harvested (crop wastes) contributes little or nothing to soil tilth because it rots on the surface and never penetrates.

We have examples of processes which turn waste biomass into charcoal and fuel gas (which could feed Clostridium cultures to make liquid fuel), and we also have existence proofs of long-term sequestration of carbon and enhancement of soil properties by addition of charcoal to soil.  We can get energy from biomass, enhance soil fertility and pull carbon out of the atmosphere; they are not mutually exclusive.