While your statement is true, this does not diminish the importance of radar altimeters: the barometer is not specific to the landing site terrain like radar is, but rather related to distance above sea level. In low visibility, radar is the only way to tell how close to touchdown you are.
This isn't really true. Before landing an aircraft gets the pressure altitude of the airport and sets their altimeters with that as a reference before landing. It's a very common procedure. These are updated regularly.
Radar altimeter is used for low-visibility approach collision avoidance and for triggering events in last few meters on AUTOLAND-equipped planes (this is rarer in USA but common for example in UK airports). The main glide slope is managed with barometric altimeter, sure, but that one lacks the detailed resolution of the radar altimeter and can't detect ground - it can only follow the difference from specific pressure according to standard model atmosphere.
While it’s true the barometric pressure is included in the ATIS information every plane will get before landing, pilots also rely heavily on GPWS callouts when landing and those are provided by radio altimeter and not the barometric one. It’s not an issue to land without them, and some approaches and emergency checklists require you turn them off to allow other messages to be announced without GPWS callouts taking priority - but it’s ideal to have them for sure.
