True, but here's what people just don't want to admit.
Traditionally there is a process for moving up the ranks. Is this process always followed? No, it's how we end up with the Tim Brewsters of the world. In addition to that, what that persons accomplishments, despite maybe not being a coach, do carry a lot of weight. Like Jason Kidd, etc. We're talking all-star, potential HoF here.
Here's the really big point. I'm sure there are reasons why your average Power 5/6 program will hire someone who was a head coach elsewhere first, followed by someone who was being groomed (associate head coach) and lastly a simple assistant coach/position coach (brewster) last for any HC opening.