The airplane was fine moments before the loss of airspeed indication, and such loss means nothing to the actual airplane itself...
I agree with PJ2 - anyone who has flown even model airplanes can tell you that a stable aircraft does not need airspeed information to continue safe flight,
All the evidence from other similar incidents is that doing nothing was a viable (and arguably the best) option. Even in alternate law the aircraft is pitch stable - the system does not use, or need, airspeed information to achieve this. This law is in fact 'graceful degradation'. Freezing the throttles also maintains the equilibrium state.
The system was never given the opportunity to show stability in roll as it was continually perturbed by pilot input. Incidentally there was no PIO - the roll oscillations are damped not divergent and the motions and stick movements are not out of phase. What we are seeing there is a pilot struggling to come to terms with a new set of unfamiliar dynamics. He got the hang of it in about 30 secs which is not a shabby performance by any standard.
As for the probes, it it clear that the amount of heat being applied was not enough to handle the rate of ice accumulation, which is a random variable. [The proposed new icing requirements show that ice concentration can be greater over short distances than long. The heating rate would have been set up to cover conditions which were less onerous than those possible. Now that a higher limit of ice particle concentration has been identified it should be simple enough to up the heating rate to cope. no need for fancy feedback systems - KISS is still a good principle]