Piracy

Private trackers have a smaller footprint and are less attractive to LE than the bigger public ones. ISPs may not be tracking traffic to the smaller sites either so you’re probably less likely to get one of those annoying “we know what you’re doing” letters using a private. Being invite only restricts the amount of bad actors(LE) that get in too.

Private trackers also have rules around seeding and have incentives to encourage more seeding, so they tend to have a good amount of them across all sorts of content.

As for anime trackers, thats out of my wheelhouse, but any good private general tracker should a decent anime collection.

Just my two cents