Also, as the heat damages the surface, it will become less smooth, which will exacerbate the heating - this cycle is probably what killed the cone (assuming the cone is what failed). Also, the time the rocket spends at high speeds and low altitudes is actually fairly long - several seconds over mach 3, and more like 10 seconds at mach 2+, based on some rough RASAero estimates (though the details depend very heavily on the sleekness of the rocket). This is an extremely demanding flight, so some of the normal assumptions have to be questioned and revisited to make it successful.
(Also, I'm not sure what you mean by "mach shadow" - the whole front surface of the cone is exposed to the freestream, and just the fact that the air passes through the shock wave doesn't do a whole lot to protect the cone)
(The math for the conical flow is here, if you're interested - the boundary layer stuff is just based on numerical code)