Cloudflare simply is making a subversive play against their competitor CDNs. Client subnet of a DNS request is used for initial rough mapping by Cloudflare competitors such as Akamai (definitely) and I believe Fastly ( and probably others) . Stripping it easily adds at least a few milliseconds to the time to first byte and most likely results a request re-routing on the second or third request.
After all, no other CDN is operating a well used public resolver.
The irony is one.one.one.one is marketed as getaway to faster internet, while making CDNs that use GeoDNS slower.
All it takes is a bad route to a far away cloudflare POP to make your internet really slower. Case in point. [1]
I really don't find why no EDNS is considered private, as it only sends the IP subnet.[2] And on IPv6 the IP is far more protected.
If you care that much about privacy, you should be using a VPN.
Another point; if you care about privacy, why use a 3rd party resolver that you have to "trust"?
Use the ISP resolver; they can see all your traffic anyway if they want to.
Alternatively, cut out all the middle men and run your own recursive resolver. It's not complicated to do so, there's other software than Bind for doing so.
https://cloud.google.com/cdn/docs/release-notes#june_27_2016