"and that can be removed and used as a building material for a new house."

I'm all for building wooden houses. But I can also imagine the amount of work (=> energy consumption) needed to convert theses trees we need to plant to "offset emissions" as new houses.

Transport the workers, feed the machines to chop the trees, the machines to transport the wood, to run the lumber-mill, to transport to the construction site etc. Unfortunately for now we still have: feeding machines => energy consumption => emissions

We can argue that this energy would have been needed anyway to build new houses. However I find it dangerous to couple a carbon reduction strategy to a substantial amount of an activity involving machines (construction). Are we going to need the amount of houses at the scale of the amount of trees we need to plant? In all parts of the world concerned (we don't want to move trees across the world anymore..)?

Unless you have a system in place to take responsibility from seed to logging to long term encapsulation I'll be highly skeptical of that.

What's to say it wont be slashed and burnt to make room for agriculture? What's to say the surplus of timber wont decrease the price and cause less trees to be planted elsewhere?

It's still sponges, not patches. They absorb the water, and you have to manage them. If you don't actively store them, the water will leak out. If you do actively store them and then hand off storage to someone else, the water will leak out when that someone stops paying attention.

The way to sequester carbon with trees is to cut them down when they're grown, and bury them somewhere where there's no air and no one will touch them for thousands of years, or otherwise store them in perpetuity while preventing decay or burning.

Turning them into biochar is a slightly simpler proposal. Biochar is stable for a pretty long time. But of course the process of unburning all the coal we burned so far is not very viable.