To make the Space Shuttle ,better' (not actually the proposed jack of all trades) it may be possible, to have created the STS an optionally manned vehicle, payload capacity of maybe 40 tons unmanned with autonomous landing, a ,stump' nose and payload bay up to the near front. For manned missions, a crew container with life support and B-70 derived escape capsules installed. Such a system might have had a higher rotation for pure payload ,commercial' (pun intended, the tried to cramp ,commercial flights' into manned missions until Challenger). Still, the Problem with tile overhaul, the unnecessary large wings, the dangerous piggyback configuration and the criminal neglect of ATK for the solids would be still there. Maybe after disaster on an unmanned mission (solids on high flight rate still likely because ATK) a return to flight might be faster.
To really improve Shuttle, one would have to go the way of ,e of pi', reusable first stage with much less heat protection needed for much lower speed at stage separation, throw away second stage (production optimized S-IV), production optimized Apollo derived crewed component, maybe later reusable winged crew component (still like the Apollo design with the ability of mission specific orbital module for satellite overhaul, logistic module for space station supply, crew/science module for long duration LEO etc.)
Eh, actually one of the MAIN requirements for the Shuttle was that it be manned and in fact that it NEED a crew for operation. In fact while the Shuttle "could" operate in an automatic mode much like the Soviet Buran, doing so required someone to manually install a cable between the flight computers and the flight systems that was not normally carried on the Shuttle. A close second was to recover the engines which were pretty expensive items in and of themselves. Really there were a LOT of know and 'assumed' requirements that went into the design of the Shuttle and once you figured in budget issues and the compromises that had to be made to meet them...
You're right that needing to be a "jack-of-all-trades" and sizing to carry larger payloads drove up the cost. As per "Right Side Up" building the booster first with expendable and semi-expendable upper stages would have had a better "return" on the initial investment. Still it needs to be kept in mind that NASA was focused on the 'future' and that drove a lot of what came to be the Shuttle we know whether those reasons are explicitly stated or not.
The "minimum" size of the cargo bay drove the size of the Shuttle which itself was derived from a future need ot carry large space station modules to orbit in the Shuttle. The wings were required for an Air Force 'need' but really NASA had already decided on the delta wings as any other wing configuration was seen as having too high a development risk. The large crew and on-orbit stay time were to get more astronauts into space and serve as a "mini-space station until a real one could be built. The "Stage-And-A-Half" configuration was driven by economics (as were most things) as the bigger an aerospace vehicle the more it costs in terms of development and production. The drop tank was the obvious way to reduce vehicle size. And since hyrdolox engines are not really efficient booster engines it was clear some sort of high thrust booster was going to be needed to get the Shuttle off the ground so the SRB's were actually an obvious choice. The Air Force had been operating large segmented boosters for years and this was thought to be pretty straight forward. They were made 'reusable' because it was hoped in the future when the SRBs were replaced by more powerful and efficient LRBs that the recovery systems would already be in place. Oh and lest we forget it is imperative, no demanded that the Shuttle be THE ONLY LAUNCH VEHICLE THE USA HAS so that any and all launches go to it. It was literally the only way to make the economics case close.
And so on.
Keep in mind that a fully reusable Space Shuttle with a huge flyback reusable booster as well as a large reusable orbiter had been the baseline concept since the beginning. This was meant to make monthly or more flights to a large space station it would help construct and maintain and would be used to deliver parts for building things like Moon and Mars ships. And keep in mind just how BIG all this was going to have to be to replace the Saturn V and Apollo capsule! Of course that's the OTHER problem is that it's going to be big, (hence by the above mentioned formula, and there IS actually a formula someplace I've seen it) and therefore more expensive than something smaller designed to JUST support a space station or perform LEO short-term tasks. The concept for making a 'cargo' and 'crew' launcher as different vehicles was suggested early on and frankly the STS design lent itself well to such a division of labor but again, in NASA's eyes if the flight wasn't manned there wasn't much point because the entire reason is to justify manned space flight. What we later knew as the Shuttle C was initially proposed by Rockwell before the Shuttle flew but set aside in order to not divert from getting the Shuttle flying first.
The Flyback F1 of RSU is a large vehicle which means it doesn't scale down well which translates into pretty large "minimum" payloads as addressed in that TL. Even if a Shuttle-C had been designed with the aim of reducing the needs of the manned element you have to consider that certain parameters have to be close to the same to retain enough commonality to remain one system. What you end up with is more a Shuttle-C with a Dreamchaser on top the cargo pod. Nice but what do you do with all that cargo space? (I KNOW we have answers but please remember this is not so obvious at the time

) Worse once you replace the SRB's and ET with a "real" reusable booster your dinky "orbiter" is going to need an expendable rocket stage to get into orbit and the whole point was to be fully reusable at the end... And can you imagine pitching THAT to Congress and the President?
Here you have this huge vehicle, these boosters fall off and land in the ocean, we recovery them. (Hopefully but given they need to be shipped back and forth to Utah don't ever expect them to be economical) The huge tank burns up, but we recover the rocket engines in a pod, (we hope) and the huge cargo volume burns up* when we're done and only this small manned section comes back to land on a runway...
(*Oh I forgot to mention a "primary" reason for the size of the orbiter as given was the idea it could retrieve satellites and bring them back down to Earth for servicing and then put them back into orbit. This required a space tug that was never built and was questionable it could actually carry, which would likely have been discarded after use since there was no space station to store it at. See how all these things tend to need each other?)
Me? My idea has always been along the lines of learning how to recover and refurbish the Saturn-1B first stage from the ocean down range to get experience with operations and costs then transitioning the S-IVB stage into a recoverable upper stage version along with a payload only version before evolving into a high reuse boost-back first stage, (still water recovered just closer to the coast, boost back to vertical landing is nice but till you get to fully 'gas-n-go' operations it's not that big a factor) coupled with either a cargo or mixed payload orbiter. Always keep the option to strap on some SRBs for thrust augmentation and you can cover pretty much anything you might need.
But in a world, (as it was) that sees "aircraft" not only in operations but in looks as the ultimate "reusable vehicle" selling that idea is an almost vertical uphill battle from the start.
Randy