I wholeheartedly agree with your post.
I've worked at companies where those in charge of hiring have focused on github profiles and in my opinion it was only ever an ego based benchmark of a candidate. Progressing or dismissing candidates on public code is not a measure of the candidate it is a measure of the recruiter.
In my current role we ask suitable candidates to complete a task from our backlog and then review this with them face to face.
It provides a standard objective form of assessment and is representative of the work we want them to do.
I believe that focusing on public repos is in the same camp as whiteboard exercises in that these practices tell the candidates more about the company and its culture than it tells the company about the quality of the candidate.
I really like the follow up you mention of sharing a screen and adding a feature and may roll this into our hiring process thanks for sharing your post!