Either I am missing something or your are mixing two topics.
Pkarr is about finding where someone writes their stuff -- which can be compared to the outbox model for "following" someone.
The "global discovery" topic is an entirely different thing, which I Bluesky solves by having one big server everybody connects to and I believe Pubky plans to address in a similar way. I believe Nostr can address that through multiple different approaches.
But when I asked you exactly what you meant by "global discovery" you said "global search", so I gave you an example of what that phrase meant to me and how it wasn't a crucial feature.
But turns out you were actually talking about "global search for pubkeys and where they write their stuff to"? I am confused.
I can answer with regards to that too, in any case, and my answer is that we hardly ever need such a thing. Learning about a new pubkey always happens within some context, and the context can often provide us with enough information such that we don't need a global registry of pubkeys and their stuff.