WeekendFlyer:
If I recall correctly there are some TAWS alerts that can trigger on approach, e.g. high sink rate or too much bank angle below a certain height. These may depend on a Radalt input to ensure they are accurate and, perhaps more importantly, don't get triggered falsely. Baro/Inertial/GPS height may not be good enough by itself, particularly when descending in the landing configuration (as you probably know, on some aircraft types with high throttle settings + full flap/slat and gear down are not usually as amenable to static pressure error correction as they are in the cruise configuration). The addition of Radalt data in to the mix improves the accuracy in the height solution for the final phase of flight.
The original ground proximity warning system that the FAA mandated as a result of the 1974 TWA 514 CFIT crash, used only a radar altimeter and aircraft configuration. That remained unchanged until the AAL Cali, Colombia CFIT accident in 1995.