Wood is wood. If you keep it dry it will last forever.

Source: carpenter

Ignoring pests, funghi, perfectly dry conditions not existing, etc.

Many of those issues are mitigated by chemically treating the woods, but that does not last forever...

And masonry also lasts forever… ignoring ground movement, frost damage, properly maintained mortar, etc.

“Old growth” wood isn’t materially better for construction along most axes, and possibly all that matter (example: modern SPF is roughly as rot resistant as “old growth wood”, but we also have way better ways to keep it dry too). Construction requires straight-enough material with sufficient flex (compression strength is a gimme) that can effectively hold fasteners. The “crappy quick lumber” that old people complain about today is actually, genuinely fine for what it is intended to be used for and fifty years from now people will be complaining about what they can buy at Robo Home Depot with the same fervor that people complain about modern silvaculture today.

I can only talk from a smaller scale. All the wood houses here are built with wood from here. Forests are strictly regulated and it's heavily illegal to deforest faster than its sustainable for the region. At least half of the people here also heat with wood, usually from their own lands. I personally have literally zero heating cost increase this year, which is crazy in Europe.

There are however at least thousands of trees for every person living here so that couldn't be scaled to a city.

Engineered wood solved that problem. Plywood is a type of engineered wood. Same for gluelams, LVLs, and CLTs. These are typically stronger than solid timber, including old growth.

It does take more energy to fabricate, but still much less than concrete and steel.