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.
It still may not be the right decision, but it's important to frame the trade-off correctly.
Every element on the network between the user and the website will know it, too.