Cloudflare has also rolled out ESNI (https://www.cloudflare.com/ssl/encrypted-sni/) which would mean someone reading your traffic would only be able to tell that you're connecting to a cloudflare IP address.
However be unable to determine which specific site you were accessing.
Why do you want to present a false sense of improved privacy by only obfuscating your DNS queries in these networks?
It seems to me like these DNS tricks are parlor tricks in a security sideshow. Any attacker that could see your packets can also see who you are connecting to. It's pretty rare that SNI does anything relevant to a real threat model.
I think a false sense of privacy is at least as dangerous as the alternative.
However be unable to determine which specific site you were accessing.