This is definitely gets more into the realm of zero-knowledge. Basically, as it stands, it is not easy to prove that the server is not censoring or tampering with the database.

DNS is a great application, especially for various decentralized naming systems, like ENS or Unstoppable. Certainly we can at least mitigate the privacy disaster that is status-quo today (people just using eth.xyz, and broadcasting every .eth domain they resolve to a random third party). Censorship-resistance is, like you said, a whole new can of worms.