Since it obviously is an issue that the insulation on the external tank
of the Shuttle tends to fall off, why not just completely do away with
the insulation?

Some sort of rapidly removed insulation could detach from the ET while
it is on the pad just before lift off. This should save weight as a side
benefit. If the heat generated in flight is too much, perhaps the
insulation in some parts of the tank could be left off and the
insulation needed for the actual flight made more robust.

Has anything like this been considered?