The problem I see here is that this FEP will not work unless everyone implements it.
I am against restricting the meaning of as:Public.
And suggest introducing an alternative as:xyz to as:Public for non-as:Public objects.
This will then also work if others do not implement as:xyz. And does not lead to objects that should not be indexed or searchable being indexed and searchable in other implementations.
I agree. Many platforms index every post they receive and store it in a database, to be served to the correct users (typically the person following the actor).
But just because it is indexed does not mean it is exposed to search.
Some platforms, such as Hubzilla, (streams), and Forte have access control and post-level permissions. Hubzilla has an account setting for called: “opt-out of search engine indexing.” And (streams) and Forte, I am told, have even more granular control over whether your posts appear in search.
Platforms already exist that give you more control over search, so this is not hypothetical.