Early in the development of the Shuttle they considered putting the SSME's under the external tank (the aeronatical engineers were saying it was very advantageous, especially early in the flight, since the thrust vectors would be more aligned with the center of mass). But they still wanted to re-use the expensive engines, so they explained that after main engine shutdown the engines needed to somehow swing over from the ET to the back end of the shuttle, allowing it to jettison only the ET. The mechanical engineers started screaming about how hard that would be, a design nightmare that would probably weigh a lot, never work well, and where any failure (engines stuck halfway) would definitely result in the loss of vehicle and crew.
I've been told that the KGB acquired a number of these design studies when their space program was developing the Energia rocket for Buran. Since they ultimately selected liquid-fueled rockets instead of solid fuel for the stack, putting the engines beneath the main tank made a bit of sense, and ironically that means the Energia stack was more viable as an HLV than Buran was as a shuttle. I really do believe STS would have had the same evolvable potential if they had taken any serious efforts to "phase in" a cargo-carrying variant: first, by keeping the stack as-is and putting the engines in a recoverable pod at the back of the cargo barge, and maybe later moving the engine pod to the bottom of the external tank to be jettisoned later.
There's one thing that occurs to me to mention at this point, an it's this: It's not that I believe that heavy lift vehicles don't have any place in the future of space exploration (the Falcon Heavy is almost that already). Actually, I'm coming around to the opinion that NASA
has no place in the future of space exploration. Even when they have access to the best engineering expertise on the planet, they are politically and systematically prevented from ever doing anything that makes sense.