Yes, the homeservers are intentionally fairly "dumb" other than being normal web servers and having features to provide info to indexers,, and "speak" PKDNS. (Note they are definitely not relays and Pubky currently does not need such a relay network like nostr uses).

Yes, you could build a full desktop app for either mirroring our indexer, or indexing on your own, but note that making your own means your app need some way of collecting and learning about keys. Once you have a key list, then you can learn the data locations and retrieve everything (something nostr can't do, discover data with keys as authority.)

I do think you'll also be interested in the app, because it is wear we will end up expressing our semantic WoT features, and you will already see the potential with the tagging UX 😉