Having many indexing features allows PostgreSQL to be useful for more types of users. Many of the indexing features are primarily useful for the GIS community, where they are used by PostGIS. BRIN indexes on the other hand will primarily help for data warehousing workloads by trading performance for reduced disk space.

And GIN indexes allows fast indexing of JSON documents and for PostgreSQL's full-text search (mostly useful for quickly adding search to simple applications).