Simply, because (it seems) there are no solutions yet available (sensors) to have the (could provide) required redundancy.
Or is it more a question of history and evolution? First: why is airspeed so relevant? (a) It is a measure of the performance of the aerofoil/airframe (stall/buffet/structural limits), (b) It allows ground speed and track to be calculated, (c) it is a convenient way to ensure separation of aircraft within the same moving mass of air.
1. Initially - given the availability of purely mechanical instruments - the pitot-static system was the easiest way to calculate airspeed.
2. As the aircraft became more complex, the system was multiplied to ensure redundancy.
3. As aviation evolved - everyone got used to using airspeed for the reasons (a)-(c) mentioned above.
4. Flight control/navigation systems evolved - in order to make them 'user friendly' (and backward compatible) designers retained airspeed as a key concept in these systems.
5. Digital data buses were introduced. To minimize the cost/risk of introducing these novel systems - rely as much on existing technology (ain't broken - don't fix it) - hence we rely on the pitot system (btw - invented in the 18th century).
Has anyone ever stepped back and asked - given today's technology - what is the best way to achieve (a), (b) and (c)? A 'clean sheet' approach, without the legacy of the past?
I find it hard to believe there is no other way (as an additional, redundant system) to measure airspeed. Even yet another pitot tube - albeit a retracting one - could provide a working alternative if all the other ones fail. But has anyone ever thought about it?
In an earlier post you could find patents filed by Airbus SAS on sensors (laser based).
Thanks - I'll try to find it ;-)