For shapefiles, FME has the ability to create a spatial index for ESRI, but of course that requires an ArcGIS license to create (and another to use).
Might I suggest creating a QGIS compatible spatial index instead/as-well? That way folks who don't have ArcGIS can still enjoy fast shapefiles.
And as a bonus (probably a different PR), FME could probably integrate the spatial index handling with "search envelope" for shape reader and read the QIX file to speed up reading in those scenarios.