Great thing about wood is you can build almost-permanent structures with it?

And the remaining biomass (leaves, bark, etc.) is fine to compost and re-enter the carbon cycle.

Also it's clearly not an open cycle, not in temperate climates. The accumulation of carbon in top soils etc. is one of the things that kept CO2 in balance for millions of years prior to us pulling it out of the ground. Peat bogs being another key one.

Yes, it can't keep up with us. But it's not an open cycle. (It is in the tropics, though)

You can build permanent structures from wood, but consider the sheer volume of wood that would be needed to counter current CO2 increase.

Best thing we can do is stop pulling it out of the ground. Best way we can do that is to build out renewables. Best way to do that is to create a profit incentive for an oversupply of power that sucks up carbon.