In a word: The kind of problems people use Berkeley DB for.
People use BDB for more fine grained cursor access to BTrees. Stuff you
CANNOT do with SQL. There is a market for this. See their website. I'd
like something similar from Postgres so that the data would be stored
in a full fledged RDBMS but I could use the cursor methods for
searching more efficient than SQL. Best of both worlds.
I've had a quick browse around the Postgres code and found some
functions like "_bt_first()" but no sample code to use it. BTW its for
developing an alternative server based access to the underlying
relational data.