I am not denying permitting exists and it slows things down. The original point was that this is a major contributor to cost of construction, which it's not. They specifically said "a small cost seems to be the actual labor and materials [compared to permitting etc]"-- this is absolutely not true. It is not even close to reality in the US.
Here you're just pointing out two facts:
1) Permitting exists (and slows things down)
2) We have a housing shortage
No argument there! But what you are failing to do is demonstrate that (1) is the major driver of (2).
The actual drivers are the cost of well-situated land, cost of labor, and cost of materials. This is evident in ANY actual budget from ANY actual construction project.
Add to that the fact that large scale homebuilders are petrified of creating a 2008-style oversupply so they've been chronically underbuilding since then -- and will continue to do so regardless of permitting reform. This is evident in the housing starts compared to population growth since the GFC.