There are several features that we would like to add that require fast retrieval of geo shapes and can greatly benefit from having docvalues support for geo shapes.

This issue has gone through a lot of evolution, so this description is edited to reflect
the latest reality

The work for adding geo_shape support for geo_centroid, geo_bounds, geotile_grid, geohash_grid aggregations was accomplished in x-pack by way of the following PRs:

• geotile_grid/geohash_grid (Add geo_shape support for geotile_grid and geohash_grid #55966)
• geo_centroid (Add geo_shape support for the geo_centroid aggregation #55602)
• geo_bounds (Add geo_bounds aggregation support for geo_shape #55328)

This is achieved by implementing by migrating geo_shape mapper registration
to a module (#53562) and then defining the geo_shape with doc values in the spatial plugin (#55037)