In response to this, I set out to see if I could patch my scales to sync to my own server.
It only supports two models of scales so far, but I got it working. My Withings scales are now syncing automatically into Apple Health over wifi, and without anything going to Withings.
Blog post: https://www.tomanthony.co.uk/blog/withings-yow-free-wifi-syn...
Github project: https://github.com/tomanthony/YourOwnWeigh/