yes, the foam iIS needed. It's there to stop ice build up. The designers anticipated that large chunks of falling ice WOULD damage the shuttle.

NASA could build a double-skinned ET but that would be heavier and cut into the payload.

Even if you had foam covers that were stripped off seconds before launch, the rate of ice build-up would be dangerous and in the several minutes of ascent through a moist atmosphere, thick ice could build up then drop off and hit the shuttle.

The basic weakness is the side-mounting of the shuttle, forced because of its big wings which were forced because of the Military's requirement for major manouevrability on re-entry.