Well .. it's not really a argument
It would be very quiet in the air if they all fail to comply to your definition of JAR 25.
Pitot is not a new technology .. icing and deicing of Pitot is not new knowledge
True and as just being a simple heated tube it can ice up upstream the drain hole; downstream the drain hole and at the drain hole itself.
All will result in 3 different erroneous Pt measurements.
I think this was enough time for find a system for alert the crew that a Pitot is out of use .. by audible or visible alarm
If the heater fails this is announced otherwise freezing is only a temporary issue.
Apart from icing it could be blocked and/or damaged by other means (bugs/birds/radome/mechanical damage).
It would need additional sensors (which are pronounced to fail by itself due to the severe environment) and computers to supply an reliable specific PITOT failure message, and - once again - all failures would lead to Pitch and Power.