The padding under the tank will have nothing to do with the rocks in the tank. Padding underneath compensates for slight irregularities between the tank and stand.
The idea behind eggcrate under the rocks is to keep the weight of the rocks from concentrating on one small area. As long as the weight is spread out, the rocks won't harm anything. Tanks set up for African cichlids have a huge amount of rocks in them.
When setting up a tank with stacked rocks, aquarium sealant is a good idea for keeping the rocks together. Falling rocks in an aquarium could lead to big problems.
The bottom supported by the sides is a strong design. Just as weight from a stack of rocks being concentrated on a small area could cause a glass failure from the inside, a small pebble or other piece of anything hard under the bottom could cause a glass failure from the other direction once the tank is filled.