I would also take this opportunity to point out that Lemmy already has full-text search.
1) Privacy by obscurity. The platform was too small for people to care, so content was sort of private, until it was put into the spotlight.
2) Social shaming as a way to maintain the above. However, others have pointed out that this does not work on bad actors, or corporations such as Google.
As a server admin, I attempt to resolve this by making it very clear in the privacy policy that all content is public. Even direct messages can potentially be public as it is not encrypted and federated to a number of untrusted servers.
Indeed, even the default Mastodon UI warns the user of such, telling them not to share sensitive information over direct messages, and when deleting their account, mentioning that their content may still (very likely) live on in other servers.
From my experiments, the user’s own pages are opted-out, but their content is federated to other servers (by design), which is then rendered on other servers without the opt-out. Or at least, where their content is part of another piece of content (eg as a reply, or as a parent post).