User will navigate to the site and show their own IP anyway. You achieved basically zero increase in privacy while making any competitor have problems with any of their users that use 1.1.1.1

And any malicious client that tries to leak data via DNS can just ask for DNS record like my-ip-is-7.8.9.0.example.com and completely go around that privacy "enhancement".

Sorry but the "privacy" here looks like smokescreen to stifle competition.