Agreed, Jig Peter. There are thousands of planes relying on pitot at this instant. Icing seems to be a rare event, and even more rare in non-Airbus.
Thanks to Sensor Validation for the OZ link, from which I quote.
On 28 October 2009, an Airbus A330-202 (A330) aircraft, registered VH-EBA (EBA), was being operated as Jetstar flight 12 on a scheduled passenger service from Narita, Japan to Coolangatta, Australia. Soon after entering cloud at 39,000 ft, there was a brief period of disagreement between the aircraft's three sources of airspeed information. The autopilot, autothrust and flight directors disconnected, a NAV ADR DISAGREE caution message occurred, and the flight control system reverted to alternate law, which meant that some flight envelope protections were no longer available. There was no effect on the aircraft's flight path, and the flight crew followed the operator's documented procedures. The airspeed disagreement was due to a temporary obstruction of the captain's and standby pitot probes, probably due to ice crystals. A similar event occurred on the same aircraft on 15 March 2009.
The rate of unreliable airspeed events involving the make of pitot probes fitted to EBA (Goodrich 0851HL) was substantially lower than for other probes previously approved for fitment to A330/A340 aircraft. However, both of the events involving EBA occurred in environmental conditions outside those specified in the certification requirements for the pitot probes. The French Bureau d'Enquêtes et d'Analyses pour la sécurité de l'aviation civile (BEA) has recommended the European Aviation Safety Agency (EASA) to review the certification criteria for pitot probes in icing environments.
Are they building the best pitot they can, or just building to (inadequate) requirements?