I never look at the Code page of projects I work on. I'm always going straight to the pull requests or issues.

I always thought the Code page's intended audience was new people checking out the repo for documentation or to peruse the code (usually after checking out the README).

I find that the code helps me get oriented, like running ls in a project's directory after cd-ing to it.

That is true, I don't really know what the answer is. You could do something like show half code/half readme, with extra code hidden behind a fold.. but I'm sure that would annoy devs working on those additional hidden files.

I'd be happy with a README-first design that had a link to move the README below the code, and that remembered which one you want on top for each repository. (Along with a preference for logged-in users to decide what they want.)

You can also put a Readme in any folder and it will show up the same way. You usually wouldn't want those up top while browsing the files though. So it's also about consistency.