Those planks and beams will still rot, burn, etc. None of this is in any way a long term solution for anything it seems.
Planks and beams rot substantially slower than they take to grow if built correctly. My house was cheap labor housing in the 1910's so no particularly fancy practice and only the exposed wood has been partly replaced. I've been told some of the beams were even recycled from Holland's old wooden shipping fleet.
That's still a temporary and limited solution. What we're pulling up now is far more and mostly won't be sequestered for countless thousands of years unless we put insane effort into making it so. Also everything about those houses has an insane footprint as of now. The steel, insulation, glass, etc It's not like you're going to outbuild climate change even if you tried.
As they rot, people would replace them, so overall captured carbon will be maintained as long as our civilization alive.
My only concern is that building those houses might actually emit more carbon than they are supposed to keep. But assuming that we moved from Oil era to Nuclear and/or Renewables, that should not happen.
It doesn't matter if it rots, burns etc -- all that matters is that it rots slower than the time it took to grow the wood it was made of
Eg:
You have a forest of trees that take 20 years to mature
You cut the trees and regrow the forest every 20 years
You use the timber to build houses (or furniture or whatever) that are _on average_ replaced after 60 years.
This will pull 3x the carbon from the atmosphere than just the forest by itself
If the structure is properly maintained and roofed it will be hundreds of years before rot is an issue. You can also design wood structures that don't easily burn, atleast not any more than large buildings are already prone to being destroyed by fire.
And are you going to continuously build houses for the sake of it? Most houses don't last hundreds of years either and the carbon being pulled up now mostly isn't going to be sequestered for countless thousands of years unless we put in insane amounts of effort making it so.