But running a service like Youtube that keeps Google in the dark about what you are watching is not possible. It's not even that content creators would have to upload their content padded and encrypted, and privately share the content with their audiences, but the entire audience would need to privately aquire the content each time. A statistically or computationally secure solution like read-only ORAM is out of question at that scale, well any scale that's larger than a few gigabytes. Anything with a constant overhead would only amount to I downloaded five videos, guess what video did I end up watching? And Google would have a one in five chance to tell, if the requests are random, but over time they could still piece you together since your privacy equals to watching five videos at a time, revisiting videos, visiting popular ones, visiting certain ones at a certain time in a certain order. The client could throw in a few fake requests, but such constant effort would still be defeated.

I can imagine a lot of interfaces for sites like that which do not require personalized feedback at all. In fact, a rich search feature allowing me to say what I want to find would usually be preferable to an opaque recommendation engine designed to steer me toward content the site wants me to visit.

There is disagreement in the cryptography community about the extent to which this is actually possible. I've seen a few proofs that the obvious "magic" version of this where you can directly but blindly search is impossible because you could use search criteria to reconstruct the content, but that only rules out the most obvious implementation strategies. There's a lot of research going on with this kind of thing in the cryptographic community that involves leveraging zero knowledge proofs, homomorphic encryption, and so on. Nothing practical enough to make anything like a blind SQL database though.

In any case I was arguing against the claim that this would preclude good UI/UX design if it were in fact possible.

When I search YouTube I’m seldom looking for all videos made on August 29th. I might instead be looking for videos of a black cat. Or videos containing music with certain lyrics that I search for. This is what I thought you meant by rich search. I contend it’s unlikely you can design a privacy respecting service that can also extract the features necessary to train a search model.