Great post for a discussion.
Yes, agree that the traditional pitot/static system is critical as it relays information required for aircraft performance. However, in the event of icing or system failure GPS information (if somehow made available) could save the day.
I don't buy the comment about the GPS system not being accurate enough - currently for GPS equipped aircraft, we can fly an RNAV approach with an RNP of as low as 0.3. 0.3NM!!! How is that not accurate enough??
In the event of a pitot/static system failure and/or unreliable airspeed, we can use the GPS groundspeed and wind information to help us. Furthermore, if they made the GPS altitude information available, though it would give us our true altitude - not pressure altitude or altitude corrected for temperature - it can give us enough information to respond accordingly. In such an extreme situation as complete pitot/static failure, even the trend (i.e. is the aircraft climbing or descending) would be enough for pilots to respond properly.
All the technology is there and available - just a matter of certification and getting through the red tape.