Eugen Rochko, the developer of Mastodon had written about Search that if it comes it should be for the home timeline and own posts. It would help a little bit,

Eugen Rochko, the developer of Mastodon had written about Search that if it comes it should be for the home timeline and own posts. It would help a little bit, at least you'd find old posts from people you follow. It would suit some, but since this is federated, there are already instances with a search like qoto.org with a full-text search. It's really odd that they made "no index" checkbox, but it's not cool to index. If they thought it is unpopular they should have made indexing opt-in not opt-out. Going forward this will be instance specific thing, a lot of people want to be able to do searches.