Secret / Private Requests

Following topic came to my mind, and I would love to discuss it:
The current DNS system is non-private and can be eavesdropped easily. Some approaches like DoH (DNS over HTTPS) or ObliviousDNS try to mitigate those risks, but they come with their own limitations.

Does ENS have any functionality to make requests in a privacy-preserving way? This is obviously off-chain, but I reckon a ECIES-based communication could make use of addresses (or NodeIDs) of certain authenticated nodes the user trusts, to make these requests.

If you are talking about look-ups, a person can of course do the look-up on the node running on their own local machine. Otherwise, the privacy always comes down to whatever other service they are using to access an Ethereum node.