What are the benefits (if any) of the new formulations for astrometry, for navigation, for astronomical data reduction, etc.?

The new developments benefit high precision applications such as Earth rotation studies. The improved accuracy will in general not be noticed by the non-specialist community. The option of working via the CEO will eliminate one redundant step from telescope-control algorithms and generally reduce "clutter" (no equation of the equinoxes, no mean and apparent sidereal time). More importantly, there is no reason why the new developments should have any "negative" impact on these communities.