stepwilk;
The use of GPS groundspeed as well as the use of GPS altitude are both short-term recommended procedures for the loss of pitot-static data. Many of us who fly these aircraft have known this for years and have probably quietly made up our own "response" to loss of pitot-static data by calmly accessing the GPS Nav data on the MCDU, (Multi-purpose Control & Display Unit) on the Airbus or its equivalent on the 777 etc.
Others have made the observation that groundspeed is not airspeed and of course this is an immediately known and appreciated fact by those who fly these aircraft, but the airplane isn't going to do anything aerodynamically dramatic (like lose/gain speed) just because airspeed data alone is lost. The aircraft was fine moments before the loss and so the key is to do nothing, except take over manually and ensure a safe flight path with unchanged thrust levels. Then assess the situation, bring up the GPS page, note the groundspeed and maintain it while the other crew member sorts the event(s) out.
What brought 447 down will almost certainly be a combination of factors/failures rather than one or another system loss, which, individually, would not be mission-critical failures.
Given this, and given the solutions can be imagined as per machinbird's comments, I think this is a promising and already-extant (in use, however informally) solution. Getting to the bottom of a rash of pitot failures would be the first in the triage sequence, however.