A few good points however I counter with the following. First the most expensive part of shuttle flight was launch not reentry. The power, fuel and resources needed to lift the craft and.recover those parts as well as the risks. Both shuttle losses involved faults at launch. The failure of a O ring seal in Challenger and the damage to the heat shield in Columbia.
its my view that both types.of accidents were and are possible with capsule type launch systems.
the only way to correct those would be to develop a new launch system either single stage or using a less risky first stage launch
second the shuttle as we knew it was obsolete by the mid nineties, however a proper follow on was delayed and then terminated. Due to first technical issues and then politics. Finally the saving grace for Dream Chaser is that its much smaller. The size of a large capsule, this is due to the large payloads already being.in orbit in the form of the ISS. This means that mini shuttle can pay dividends by removing the need for specialized boosters and allows the return to the easy recovery of the shuttle that with a intact heat shield is much less expensive then the complex search and rescue operations demanded of water and land drops.
The biggest problem with the shuttle was indeed the launch, specifically the cost, at >$7,000 per kilogram, of having to launch an additional 90 metric tons of aerodynamic shuttle airframe into space along with a mere <25 tons of true mission payload.
This basic proportion of launch cost burnt to send up the dead weight of an aerodyanmic shuttle to launch cost incurred in actually launching the payload, hasn't changed, even if the shuttle orbitor itself is long on the tooth.
You are incorrect in saying either of the shuttle diseasters were caused by faults that would have been there with an expendable booster. In fact both the challenger and the Columbus diseasters were directly attributable to a massive yet totally insufficient design compromises adapted to slightly lessen the totally incompetitive cost of launch the dead weight of the shuttle along with actual payload by making as much of the launch hardware recoverable and reusable.
Let's start with the Columbus diseaster. The columbus diseaster was directly caused by the fact that the shuttle orbitor rids piggy back on the side of the liquid fuel tank rather than on top, as would be the case with a capsule sitting atop an expendable booster. This allowed ice and insulation from the tank to rain down upon the shuttle orbitor during lift off, and knock holes on the reinforced carbon carbon heat protection on the leading edge of the wing.
The reason why shuttle rides so awkwardly on the side of the fuel tank was to enable the liquid fired space shuttle main engines (SSME) to be attached to the back end of the shuttle orbitor, and thus be recovered rather than lost with each launch. A capsule would be economically competitive without resorting to this disparate measure, the shuttle was uncompetitive even with this measure.
Now look at the challenger diseaster. Yes, the O-ring failed. Yes, the launch occurred when atmospheric temperature was too low to allow o ring to retain flexibility and to enable the O ring to seal properly at the moment of ignition. But why did the O-ring need to seal so well at the moment of ignition? Again, it came back to the piggy back configuration of the shuttle launch stack which later would doom Columbus by another means. With normal solid rocket boosters, ignition would expand the steel casings and cause the tong and groove joints in the casing to self seal, and the O rings wouldn't need to be very flexible until it is heated up by solid rocket burn. But on the space shuttle, the liquid fired main engines (SSME) were not in line with the solid rocket boosters, nor did they fire after the solid rocket booster burned out, as would be the case with a expandable booster. Instead are off set way to one side of the solid rocket boosters, and fired just before the solid rockets ignited. As a result of shuttle stack configuration, when the SSME fired, it rocked the entire shuttle launch stack to one side, and significantly bent the solid rocket boosters, whose base was still rigidly fixed to the launch platform, at the moment when the solid rocket booster itself was about to ignite. This bending flexed the solid rocket booster casing, and opened up each steel tong and groove joint in the casing just as the booster ignited, thus forcing the O ring to perform the main work of sealing the joint. It was this reason that made the failure of the O ring fatal. O ring was too cold to flex and fill the gap, the hot gas didn't meet a pressure resistence, so were able to burned a trench through the tong and groove steel joint.
So it is the cost of launch that doomed the shuttle economically. It is severe yet inadequate design compromises adopted to slightly reduce this launch cost that doomed two shuttle orbiters physically.
A small Chinese recoverable shuttle that sits on top of a expendable booster would get around the ice problem and the o-ring problem the doomed Columbus and Challenger, but it would not get around the 4 tons of dead weight for each ton of payload problem that made the whole US shuttle program into essentially a massively costly and economically unviable make work program for NASA.