I think this problem is much more scientifically solved by applying classical mechanics. Friction is obviously key over here as that's what's causing the tyres to bald.
Let's first look at the way we calculate kinetic friction:
$f_k = \mu_k N$
Pretty simple right? N is the normal contact force experienced by the body for which we're calculating the friction experience by it from the surface. $\mu_k$ is the coefficient of kinetic friction and is a constant for two surfaces. But look here, there is no effect of velocity influencing the amount of friction experienced for an ideal tire (i.e, a tire which retains its shape regardless of heat applied on the tire from friction).
So, moving with high velocity in a straight line is not likely to damage the tire. While there may be some credibility to the other answers explaining how the surface area of the tires (and consequently friction) expands when moving at high speeds, there is no evidence that the friction during high linear velocity itself will make a difference because the kinetic friction is constant for a moving object, regardless of its velocity.
But, what if we consider circular motion?
I imagine that a good part of Pirelli's data came from testing their tires on circuits. A good part of most racing tracks consists of turns. And here, the velocity makes a difference.
Let's look into the mechanics of how this works:
For a vehicle (or anything for that matter) moving in a circle with some constant linear velocity, it requires an acceleration towards the center of the circle. This acceleration changes the direction vector of velocity and is called centripetal acceleration.
...and it is calculated by the expression:
$a_c = v^2/r$
Multiplying by mass, we get centripetal force:
$F_c = mv^2/r$
Now, when a vehicle moves in a curved path, the static friction between the tires and the road prevents it from sliding off the circular path. It's easy to imagine that if there wasn't enough friction, the vehicle would slide and crash against the walls of the circular track.
Static friction is given by the same expression as kinetic friction (except $\mu_s$ is a variable coefficient and depends upon the sum of forces acting on the object:
$f_s = \mu_s N$
And this $f_s$ is providing the centripetal force.
So, $f_s = mv^2/r$
Here, we can see that friction will depend on the square of the velocity of the vehicle! So taking sharp turns at high velocity will create a lot of static friction between the tires and surface, wearing them out much faster!
So yes, driving at high speeds will definitely wear the tires out faster when taking turns, whereas it won't make a big difference when driving in straight line.