How about the situation when the documentation has to be prepared before any of implementation or coding starts (initial requirements, qc etc.) ?

I think it's fine to document these things in Sphinx as well. Creating a docs repo and writing .rst files to cover these requirements can be useful, and then you can move them as needed as your project progresses.

I'm using Latex for exactly that, but it sucks so much I considered building a product/business to solve the problem.

I guess you still have to use SC to be able to pickup changes by others right?

Sorry, what is SC?

code Source Control...