Think less "private" and more "protected." Like Patreon subscriber perks, paywalled content, or just someone who only wants certain people to see what they post.

Who would you ask besides the author's PDS though? Would every relay have a cached copy of all private data, but only give it out after checking auth? That's not a very safe design - what if my relay doesn't check?

spaces do not use relays. The sync protocol is pull from PDS. https://dholms.leaflet.pub/3mqtqvjidqs2p

So it's a central server and doesn't benefit from being ATP as it can be anything you want.