Ah thanks for the link! I didn't know the term for "natural hugelkultur."

I don't mean to denigrate hugelkultur, rather just point out it's a folk practice based on mimicking a well understood natural process. Since it's largely used for hobby farms and gardens where enjoyment is far more important than yield, it hardly matters whether it's a folk practice or the latest agtech discovery. Just be careful not to cause drainage issues with all those berms slowly eroding! Nature can take advantage of that process optimally while in your yard it might just cause a damper basement.

Another way to ask this: how does hugelkultur logs/material compare with a similar volume/mass/cost of other material e.g. traditional soil.

My guess is it does pretty well: traditional soil struggles to retain water, which can be scarce and even when it's plentiful water is difficult to optimize for high density gardens, especially urban gardens.

If I understand the hugelkultur design, the sod/straw layer keeps the berm from eroding.

Beneficial to those plants which do not belong to the sort of early succession. They need disturbed sites and bare soil.

Some of the bread and butter trees of aggro-forrestry establish better on bare soil rather than a thick layer of humus from decaying trees.

From what I understand, it gives long lasting benefits.

One of my mentors is a soil scientist that has been doing ecological restoration for over 30 years. He tells this story of where he had to walk across a mountain range pushing a long metal rod into the ground every 3 meters. While most places barely took the probe, the places where there were nurse logs he could sink them deep in all the way.