I agree with this 100%. However, to be useful it needs to hit the right level of crudity. For most projects, a short (<10 pages) description of goals, design principles, architecture and an overview of interfaces is sufficient.
It is best when this exists as a standalone document which is a required reading for any new developer. After this they can look at module descriptions, function docs, code, etc. and understand how to make sense of it and how to add their code without breaking general principles of the project.
> Ideally it should be in version control and be generated from the code, because then it's less likely to go out of date.
With this, I have some beef. In my experience the best documentation is the one that complements the code. Usually this means a short description by a human that explains what this chunk of code does and assumptions or limitations (e.g., "tested only for points A and B in troposphere") and IME most useful information is not derivable automatically. Auto-generated docs are very useful, but cannot replace clean explanations written by a human. My 2c.