They have their place in the big picture.
In most cases, they were originally designed for off road and other racing activitites. In those cases, they were not padded as the transmission of noise wasn't relavant.
In a street car, the advantages is that it helps to control torque movement from your drive train. When you step on the gas, rotational movement has to be translated into linear movement, in so doing, the engine and transaxle are trying to rotate sideways as well as rotating around the axix of the axles. These straps help to eliminate broken transaxle mounts due to rotational forces. Also, if stock mounts should break, they help in keeping the transaxle/engine attached to their mounting horns.
They do have a drawback in that they will transmit some noise regardless of the padding but in my opinion, it's a small price to pay especially if you have a hot rod engine that's putting way more force on the transaxle mounts then they were originally engineered for.