I missed your comment, it's better reasoned than mine and I think I agree with it.
I was just saying on another comment that I think the problem is GitHub, while maybe it shouldn't be, is the de facto project page for many projects, and is a major use-case.
There perhaps can't be a good solution - it's convenient enough that most small developers can't be bothered maintaining two different information sources about their work, and GitHub certainly has no reason to dissuade people from using it that way, but to prioritise the readme would make actually using the site harder.
Just one of those awkward things you live with, perhaps.