Elasticsearch in particular can do the kind of queries most people expect from a database, see
https://www.elastic.co/kibana/
At work we have a search interface powered by Postgres that uses the full text index but also uses GIN indexes on arrays to index things based on categories/tags.
What's the difference?
> Heuristic search is going to be non-exhaustive by definition.
To me, a non-exhaustive search is broken by design, because it will miss results. Making data accessible only through such search means there will be a hole in the system into which some of the data falls, never to be seen again.