I have visitor statistics enabled on my site and I like to see how many visits I get on articles. The point is to not see more in it than it can tell you, so I don't really understand the 'remove all statistics because it doesn't matter' argument.
- If the analytics don't change the way you write, then they are useless overhead.
- If they change the way you write (because you try to maximize the number of views), then they may be toxic.
IMO you should write what you have to say, not what you believe people will want to read (with the help of tracking).
When I realized that, I removed GoatCounter from my website, which is now a minimal, static, no-javascript, no-tracking personal blog. And it feels good.
However, I must say your idea is a very good one!