. We conduct external pre-flight inspections all the time with the covers on as they are removed by Mx personnel closer to departure time.
Our (Airbus) covers are woven from kevlar, and I don't get the sense that anything short of an oven would compromise them. In fact they are made specifically not to melt; perhaps there is something about their construction that makes them unravel?
The screens don't go blank during an unreliable airspeed event....in fact pilots are expected to fly attitude and power to a safe conclusion.
There is also a back-up speed scale that, when selected by turning off air data, displays fast/slow cues based on alpha. That system (BUSS) may in fact be a a factory option, and if so, MH may not have it installed* (see below)
Unreliable airspeed in an A330 is a non-trivial, but manageable event. That said, its pretty unlikely to cross the fence at exactly the optimum speed, and a heavy, slow aircraft bleeds energy quickly. Its not difficult to see how either a hard or long landing might result, especially with rarely used manual thrust.
On edit...I was curious about the BUSS. Deeper research reveals that BUSS might be optional even on later build aircraft.