While this is true (and a problem with current engines like Google), I could see having a local LLM doing the filtering for you based on your own criteria. Then you could do a wide-open search as needed, or with minimal filtering, etc.
When I'm searching for technical stuff (Android rom, Linux commands/how it works), it would be really helpful to have some really capable filtering mechanisms that have learned.
When I want to find something from a headline, then it needs to be mostly open (well, maybe filtering out The Weekly World News).
But it really needs to be done by my own instance of an LLM/AI, not something controlled elsewhere.