A search engine presumably has 2 things, a database and a search algorithm
The user doesn't have direct access to the underlying database
Sometimes when I'm searching something, I want to do some very specific and unusual filtering and the built in filters/settings just aren't enough. It would be impossible (or at least crazy) to include all the different possible settings that I might want, you'd practically be writing a new scripting language.
However databases are important and common enough that they already have specific languages for querying them, like SQL. Where filters and settings wouldn't be enough, SQL probably would.
So what I really want is direct access to Google's databases (because it presumably has the biggest and this comes up when I'm looking for something really obscure). But I'm guessing that's not gonna happen.
https://blog.kagi.com/small-web
https://search.marginalia.nu/