I think it is mostly fine if this search only works on public posts and respects post deletion. I understand it may be misused, but almost every feature of Fediverse software can be misused as well, and I myself really think search of public posts is a useful feature for finding older posts that can contain useful information.

Making some flag for indicating of post should or should not be searchable by instances (not by search engines since already have an option in profile) in addition to content visibility would be nice, but well, only if someone would actually make it and search capable software would start respect it.