The throughput of carbon sequestration per unit of time is a direct function of the quantity of gallium and the time it takes to execute a complete reaction cycle. Whether or not you recycle the gallium, the time it takes to complete the process cycle limits the number of iterations you can execute per year, which in turn limits the amount of carbon a ton of gallium can sequester per year.

If you need to remove tens of gigatons of carbon per year, you are going to need similar scales of gallium to have enough reactant operating concurrently.