Yes. This would change the aerodynamic properties of the wings in unpredictable, uncontrollable ways. All it takes is for a few unburned patches of the material to remain to make it very difficult to control the trim of the shuttle during re-entry.
I've seen a hard shield over key areas proposed that could be jettisoned, but that in turn could cause damage as it was jettisoned, along with leaving vulnerable points where it connects to the shuttle.
Yes, and that is why I suggested that structural foam. If you ever saw that stuff burn it is amazing! It seems to vaporize. It will disappear completely at a fairly modest temperature, such that there will be nothing left of it long before it runs into any significant atmosphere. It might even need the second, harder outer coat to make it through takeoff. The big benefit is keeping the tiles covered and undamaged until they will be used and then completely disappearing long before the temperature gets high.