This AD does not mention icing per se. A blocked AOA probe does not necessarily mean it was iced up in icing conditions. One can refer to the Perpignan crash, as previously posted. The AOA probes 1 & 2 were blocked in clear weather, due to improper maintenance while washing the aircraft: a high pressure water jet was used to clean the fuselage, and water passed throught the first seal to lodge within the AOA probe's casings. Only after spending some time at altitude did the probes block up because the water inside the casings of AOA 1 & 2 had frozen up. Again, not ice accretion.
Due to the voting system logic, if two probes read "X" value and a third one reads "Y" value, the Y will be considered erroneous, regardless of the reality. There is no other way for the system to assess wrong ADR inputs/outputs.
This is where a pilot comes in handy. If you are lucky enough to get sufficient time to identify the failure before getting into a nose dive and and exceed VD, turning off two ADRs has a dual function: with only one ADR, the autoflight reverts to alternate, as previously mentioned, so speed protections are lost and the pilot will recover flight control authority, with the possibility of manually exceeding any high or low speed regime, as well as bank angles. That is just the way airplanes flew before FBW for the last 100 years almost. It's up to the pilot to keep the aircraft within the flight envelope.
The second function, is to force the system to use only one ADR source, thus removing any voting logic out of the equation. This should be a momentary solution, as the pilot , unknowingly, may have kept ON the ADR with a blocked AOA. Therefore, after full flight control authority has been recovered, investigating which of the ADRs has blocked AOA would be greatly beneficial, in order to get the SW working should other sh*te happen on the same flight.
This is one of the reasons I have no time for pilots saying "We don't need to know the system in that much detail" or "I don't need to know that". We are not mere button pushers. Anyone not interested in aircraft systems should not be flying airplanes for a living. Imagine a soldier going to war, and doesn't care how his automatic rifle works, and says "nah, it's OK, you just need to pull the trigger, should work fine." See how far this soldier would go...