There are several major problems this solves. The forests are overstocked, which is part of what leads to larger and more severe wildfire. These are live trees, and won't break down, but need to be thinned. And if the forest does burn, that dead wood needs to be removed to prevent it from burning again. This wood could break down eventually, but it makes it riskier to replant (for both the people planting, and the new seedlings).

Both of these activities are incredibly expensive, and burying the trees in a vault on site could provide a way to manage all of the wood, and pay for it.

Should wood vaults be the only solution? Probably not. And we should definitely remain skeptical as they are proven out. But proper forest management is challenging, expensive, and is often neglected (at least in the US), and I think it's overall beneficial to explore novel solutions like this.

Hopefully one where they are not burned or decomposed. Still, I think when applied to otherwise decomposing wood, the approach is interesting, as a transitional measure anyway.

How is this wasting the wood? The wood is directly available to insects and fungus once it's buried

In much of the western US, subterranean termites will eat buried wood.

Fire.