Piggyback isn't the problem
The main design flaw with the STS system is that the main engines are located on the orbiter. Had the main engines been located under the ET, then we would've had a heavy lift launcher that could also pull double duty as the launcher for the shuttle.
Imagine for a moment if we had an Energia type launch system. It would be a stand alone heavy launcher that could also launch shuttles as needed. Shuttles could be built and replaced with newer models as technology advanced without disrupting the opertations of the core launcher. It would give us flexability on a level never before seen. Why Nasa can't see this is a mystery.