At first, I wondered why radio altimeters were such a big issue. You have both a barometric altimeter, which is usually set to the local pressure, and on approach you have at least glideslope. During the time I flew general aviation (US), two of my airplanes had radio altimeters, and I never used them except for amusement.
One problem is that when flying into airports in the SW and mountain states, the surrounding terrain can be well below the airport's elevation. That might be bad, if one descended to 200 feet AGL before reaching the threshold. Then I looked at the AD notices. Apparently, in modern airliners, the radio altimeter is linked to important landing functions, such as reverse thrust and automatic braking. The two "passengers" in the front seats cannot control those independently.
Once obvious solution seems to be ignored. Why not have the pilots make those decisions?
I'm not a pilot, but I am pretty sure spoilers and autobrakes are typically triggered by the weight-on-wheels sensors, not the RA, and reverse is typically manual (though gated by weight-on-wheels), though there are probably some aircraft out there with different logic. These systems are armed manually or possibly by the aircraft during a managed approach (which might use RA to decide, but could easily use the INS altitude or some other signal), but activated when the aircraft touches down. If there's one lesson to take from the decades of aviation safety improvement, it's that humans are fallible, slow, and easily distracted, so reducing workload with automation is almost always a safety win. Having pilots do things manually would increase the amount of errors, both in the tasks themselves, as well as other errors caused by the increased workload during an already high workload phase of flight.
The biggest user of RA is one that can't be replaced with something else - EGPWS, which is a safety system designed to save the plane when the pilots have lost situational awareness. Obviously, given its purpose, you can't replace this with pilots, and it depends pretty heavily on RA.
It also provides altitude callouts (50-40-30-20-RETARD) which aid pilots in timing the flare, reducing human factors on landing performance, and the higher altitude ones provide procedural checkpoints. Also rather obviously essential for autoland. Of course you can get away without it, but you'll have sloppier landings and likely need increased minimum landing distances to account for that.