The whole thing? That is what Agile Manifesto, and the associated 12 principles, is about: A thought experiment about flat organizational structures. Each of the 12 principles outline the things one needs to consider when they don't have a manager taking watch.
Where you find a VP, Agile isn't applicable. At least not in its entirety. It it is likely that you can still cherry-pick some ideas from it to apply to your non-Agile situation. "Do your manager's job for them" is often considered common wisdom after all.
You must have worked in some very unhealthy teams where psychological safety wasn't present. I'm sorry that happened. But don't confuse your experiences with that of everyone else's. There are lots of teams that are agile from the top down, including those that happen to hold a title with VP in the name.
Where you find a VP, Agile isn't applicable. At least not in its entirety. It it is likely that you can still cherry-pick some ideas from it to apply to your non-Agile situation. "Do your manager's job for them" is often considered common wisdom after all.